The present invention relates to apparatus and a method for determining
the sum of first and second optical binary words, each word having a number of
optical bit slots.
In the field of all optical processing, optical signal streams are
used for data processing applications. These optical streams consist of an optical
pulse train that is divided into a series of bit slots. Each bit slot, which has
a predetermined length within the pulse train, represents a single bit of data,
with the presence or absence of an optical pulse within a bit slot representing
complementary logical states. Thus, for example, the presence of a pulse may represent
binary "1", whilst the absence of an optical pulse may represent a binary "O",
or vice versa. In this specification, therefore, we use the terminology "optical
binary word" to mean a binary word represented optically in this manner.
One of the basic optical processing applications which is required
is the ability to generate the binary sum of two optical binary words each word
consisting of a number of bit slots.
Optical serial counters are known (VP Heuring et al, "Bit-serial
architecture for optical computing", Applied Optics, vol. 31, no. 17, 10 June
1992, pp 3213-3224), having a number of optical switches and two circulating loops.
According to a first aspect of the present invention as defined in
independent claim 1 we provide summing apparatus for determining the sum of a first
optical binary word and a second optical binary word as defined in independent
claim 1.
According to a second aspect of the present invention we provide a
method of summing a pair of optical binary words as defined in independent claim
11. Further embodiments of the invention are specified in the appended dependent
claims.
We have designed apparatus and a method for generating the sum of
first and second optical binary words. This is achieved by generating first and
second output words representing first and second logical combinations of the
optical binary words, using the first and the second optical logic elements respectively.
These optical output words are then offset with respect of each other and recombined
to generate further output words. By repeating this process until each bit slot
of a first output word has the same logical state, the binary sum of the first
and second binary words can be determined.
Typically the first and second optical elements logic have first
and second inputs for receiving the binary words to be combined, although a single
input could be utilised with the binary words to be combined being applied consecutively.
Preferably there are provided means for repeatedly applying the previously
generated first and second output words to the first and second logic elements,
comprising a connection from the output of the first logic element to the second
inputs of the first and second logic elements, and a connection from the output
of the second logic element to the first inputs of the first and second logic element.
This is effectively a feedback system, with the combination word generated at
the output of each logic element being fed back to an input of both logic elements.
Alternatively however a feed forward system can be employed in which
the means for repeatedly applying the previously generated first and second output
words to first and second logic elements comprises N first and second optical
logic gate pairs, each first and second optical logic gate pair comprising a first
optical logic gate which generates a first combination word representing a first
logical combination of binary words applied thereto, a second optical logic gate
which generates a second combination word representing a second logical combination
of binary words applied thereto, and offsetting means for offsetting the first
and second combination words by one bit slot with respect to each other to generate
first and second offset combination words, wherein the offsetting means is coupled
to the downstream first and second optical logic gate pair such that the generated
first and second offset combination words are applied to the first and second
logic gates of the downstream first and second optical logic gate pair.
In the feedback system the offsetting means typically comprises an
L bit slot delay line coupled to the output of a first optical logic gate and either
an L+1 or an L-1 bit slot delay line coupled to the output of a second optical
logic gate. Whilst any suitable method of introducing a one bit slot delay may
be used, it is very difficult to introduce single bit slot delays at high bit
rates. Accordingly, it is preferable to use L and either L+1 or L-1 bit delays
allowing a one bit slot offset to be generated between the relevant optical binary
words. Furthermore by using L and L+1 or L-1 bit slot delays, the output words
can subsequently be fed back to the inputs of the logic gates without interfering
with the previously input words.
The use of the L+1 or L-1 bit slot delay will depend on the format
of the optical binary words. Thus if the first bit slot of the optical binary word
represents the lease significant bit of the binary numbers to be added, then the
L+1 bit slot delay is used. On the other hand, if the first bit slot represents
the most significant bit then the L-1 bit slot delay is used.
For ease of discussion the remainder of the specification will discuss
examples in which the first bit slot represents the least significant bit of the
binary numbers to be added, unless otherwise stated. Accordingly, the use of the
L+1 bit slot delay will be assumed, although it will be appreciated that for a
different optical binary word format the L-1 bit slot delay would be used.
Typically, in the feedback system, the connection from the first
logic gate to the second inputs of the first and second logic gates comprises the
L bit slot delay line, and wherein the connection from the output of the second
logic gate to the first inputs of the first and second logic gates comprises either
the L+1 or the L-1 bit slot delay line, although additional connections may be
employed.
Preferably the feedback apparatus further comprises an optical combiner,
the optical combiner having a first combiner input coupled to the L+1 bit slot
delay line, a second combiner input which receives the first and second optical
binary words, and a combiner output coupled to the first inputs of the first and
second logic gates.
Whilst the optical combiner is not required for calculating the sum
of two optical binary words, the presence of the combiner does not effect the operation
of the circuit. Furthermore, as will be explained below, it is sometimes desirable
to input more than two optical words to the circuit. In this case, the combiner
is provided to prevent interferometric mixing of the optical word supplied to
the circuit with the optical pulses already present in the circuit.
The optical combiner operates by combining bit slots received at
the first and second inputs such that if the bit slots have identical logical states,
the combiner output generates a bit slot having the first logical state and if
the bit slots have different logical states, the combiner output generates a bit
slot having the second logical state. In use, this allows the first and second
words to be supplied in sequence to the second combiner input such that the first
and second words are supplied respectively to the first and second inputs of the
first and second optical logic gates.
In the feedforward system, the offsetting means typically comprises
an M bit slot delay line which couples a first logic gate to the second gate inputs
of a downstream first and second logic gate pair, and an M+1 bit slot delay line
which couples a second logic gate to the first gate inputs of the downstream first
and second logic pair such that the transfer of a first output word from the first
gate is delayed by one bit slot with respect to the transfer of a second output
word from the second gate. Whilst any suitable method of introducing a one bit
slot delay may be used, it is very difficult to introduce single bit slot delays
at high bit rates. Accordingly, it is preferable to use M and M+1 bit delays,
for M>1, allowing a one bit slot offset to be generated between the relevant
optical binary words.
Again, as described with respect to the feed forward system an M-1
bit slot delay line could be used instead of the M+1 bit slot delay line if the
format of the optical binary words has the most significant bit in the first bit
slot.
Preferably, the Nth first and second logic gate pair comprises feedback
apparatus with the M bit slot delay line of the Nth first and second optical logic
gate pair being constituted by the L bit slot delay line and the M+1 bit slot
delay line of the Nth first and second optical logic gate pair being constituted
by the L+1 bit slot delay line. Such an arrangement combines the advantages of
both the feedback and the feedforward aspects of the present invention.
Preferably, each first logic gate comprises an AND gate and wherein
each second logic gate comprises an XOR gate. It will be realized however that
the invention could be implemented using complementary logic, in which case alternative
logic gates, such as XNOR and NAND gates, would be used, the terms "AND combination"
and "XOR combination" being understand to include such complementary logic.
Typically each optical AND gate comprises an all optical non-linear
gate, wherein the application of a bit slot having the second logical state to
the first input selectively switches a connection between the second input and
the output for a time interval corresponding to a single bit slot so as to transfer
a single bit slot from the second input to the output, whereby a bit slot is generated
at the output representing the logical AND of the bit slots received by the first
and second inputs. This provides a simple means for combining optical words to
generate the logical AND of the two words.
Typically each optical XOR gate comprises an optical combiner, the
optical combiner comprising a first combiner input coupled to the first input of
the XOR gate; a second combiner input coupled to the second input of the XOR gate;
and, a combiner output, wherein if the bit slots received at the first and second
combiner inputs have identical logical states, a bit slot having the first logical
state is generated at the combiner output and wherein if the bit slots received
at the first and second inputs have different logical states, a bit slot having
the second logical state is generated at the combiner output. This apparatus provides
a simple way of generating the logical XOR of first and second binary words.
Typically the XOR gate further comprises a source which generates
a stream of bit slots having the second logical state and, an all-optical non-linear
gate, the non-linear gate comprising a gate input coupled to the source, a gate
output coupled to the XOR gate output and, a gate switching input coupled to the
optical combiner output, wherein the application of a bit slot having the second
logical state to the gate switching input selectively switches a connection between
the gate input and the gate output, for a time interval corresponding to a single
bit slot, so as to transfer a single bit slot from the gate input to the gate
output. This ensures the optical quality of the optical word representing the logical
XOR of the combined words is of good quality and is in the correct format for
use by the rest of the circuit.
Typically the second logical state is defined by a bit slot containing
a single optical pulse, although this depends on the specific implementation of
the circuit and it is therefore evident that a bit slot containing a single optical
pulse may define the first logical state.
Typically the first combination word represents the binary sum when
each bit slot of the second binary word has the first logical state, although again
this depends on the specific implementation of the circuit.
Typically the method of the invention continuously repeated until
each bit slot of the second combination word has the second logical state, although
this will depend on the implementation of the methods.
Preferably, the second logical state is defined by a bit slot containing
a single optical pulse; although a bit slot containing a single optical pulse may
define the first logical state.
Examples of the present invention will now be described with reference
to the accompanying drawings, in which:-
- Figure 1a shows a schematic representation of a delay line;
- Figure 1b shows a schematic representation of an optical combiner;
- Figure 1c shows a schematic representation of an all optical non-linear gate;
- Figure 1d shows a schematic representation of an optical pulse source;
- Figure 2 shows a schematic representation of a binary adder according to the
present invention;
- Figure 3 shows bit slot time lines indicating the presence of optical pulses
at several locations around the binary adder of Figure 2;
- Figure 4 shows a schematic representation of the configuration of the logic
gates used in the binary adder of Figure 2;
- Figure 5 shows a resettable binary adder, which includes the binary adder of
Figure 2 coupled to a window generator;
- Figure 6 shows bit slot time lines indicating the presence of optical pulses
at several locations around the window generator shown in Figure 5;
- Figure 7 shows bit slot time lines indicating the presence of optical pulses
to several locations round the binary adder of Figure 2 for an alternative input
pulse stream;
- Figure 8 shows a schematic representation of the configuration of the logic
gates used in a binary adder according to a second embodiment of the present invention;
and,
- Figure 9 shows a schematic representation of the configuration of the logic
gates used in a binary adder according to a third embodiment of the present invention.
In order that the invention be understood, certain symbols have been
used in the Figures relating to the description. These symbols are shown in Figures
1a to 1d and their meanings will now be discussed.
Figure 1a shows a delay line 1 which operates to delay the transfer
of an optical pulse stream applied at one end of the delay line 1 to the other
end, by a predetermined time interval. This time interval usually corresponds to
a predetermined number of bit slots. The delay is achieved using either a length
of optical fibre, a silica plane waveguide, or a free space path, or the like,
such that the optical pulse takes a predetermined amount of time to travel the
length of the element.
The length of delay on a delay line will depend upon the physical
length of the waveguide, free space path, or optical fibre used and also the refractive
index of the particular transmission media (which will effect the speed of light
within the media).
Figure 1b shows an all optical combiner 2 which has two combiner
inputs 3, 4 and a combiner output 5. The combiner 2 combines two optical pulse
streams applied to the two combiner inputs 3, 4 in a way that avoids interferometric
mixing of pulses.
In practice this is usually achieved by having the pulses of the
two different pulse streams arranged at different positions within the respective
bit slots, such that the pulses do not overlap in time but are still in the same
bit slot. Alternatively however it can be achieved by having orthogonally polarised
optical combiner inputs, with the received optical pulse streams having at least
some components which will pass through the polarising elements.
As a result of this non-interferometric mixing of pulses, the total
optical energy output from the optical combiner during any one bit slot is sum
of the total optical energy received.
The optical combiner will usually take the form of an optical fibre
coupler, a silica planar waveguide, or a bulk beam splitter.
Figure 1c shows an all optical non-linear gate 6 which is a form
of non-linear optical switching element such as a fibre non-linear optical loop
mirror (NOLM), a fibre NOLM with an offset semiconductor amplifier, or an integrated
planar NOLM. Mach-Zender, Michaelson and time-division versions of these devices
are also possible although will not be considered in detail in the specification.
One specific type of optical switching element of this type is the terahertz optical
asymmetric demultiplexers (TOADS), which are described in the paper entitled "Asymmetrical
Optical Loop Mirror: analysis of an all-optical switch", Applied Optics, Volume
23, No. 29 1994.
The all optical gate has two gate inputs 7, 39, two gate outputs
8, 9 and a gate switching input 10. Each gate input 7, 39 is connected internally
to a respective gate output 8, 9, with the connections depending on the state of
the switch. Thus, when the gate is in an unswitched state, the gate input 7 is
connected to the gate output 9 and gate input 39 is connected to gate output 8.
However, when the gate is in a switched state, the gate input 7 is connected to
the gate output 8 and the gate input 39 is connected to the gate output 9.
In operation, the state of the switch is controlled by the application
of optical pulses to the gate switching input 10. This is achieved using an optical
pulse stream comprising a number of bit slots, the stream containing a number
of optical pulses. These optical pulses are received by the gate which operates
to integrate the total optical energy received over a predetermined time period.
From now on, it will be assumed that this time period corresponds to a single
bit slot, although in certain circumstances, longer or shorter time periods may
be preferable.
Thus, for example, if a single optical pulse has a total energy E,
and a bit slot containing a single optical pulse was applied to the gate switching
input 10, then a total energy E would be detected. However, if two optical pulses
were present within a single bit slot, then the switching input would detect a
total energy 2E equivalent to two optical pulses.
The gate has an approximately sinusoidal response to the total amount
of energy received during the predetermined time period, such that if the total
energy received is an odd integer multiple of the energy contained in one optical
pulse, then the switch will enter the switched state so as to transfer any data
received at one of the gate inputs 7, 39 to the respective gate output. The gate
will return to the unswitched state at the start of the next bit slot. If an even
integer multiple is received the switch will remain in the unswitched state.
There is however a limit to the number of optical pulses that can
be detected during any one time period. Accordingly, to avoid miscalculation of
the number of pulses received, it is preferably ensured that no more than two
optical pulses will ever be received by the switch during a single bit slot. Consequently,
the switch will only enter a switched state if a single optical pulse is received
during the bit slot. Such a bit slot containing a single optical pulse for application
to the gate switching input 10 is hereinafter referred to as a switching signal.
Thus, with none or two optical pulses applied to the gate switching
input 10, during a bit slot, an optical pulse stream provided at the gate input
7 will pass through the all optical gate to the second gate output 9. However
the application of a single optical pulse to the gate switching input 10 will act
as a switching signal causing a single bit slot of the optical pulse stream applied
to the gate input 7, to be diverted from the second gate output 9, to the first
gate output 8. Any further bit slots in the input optical stream will continue
to be output from the second gate output 9 unless further switching signals are
received.
In logical terms, the gate 6 operates such that reception of a bit
slot containing one optical pulse is equivalent to receiving a logical signal of
one logical state, whilst reception of a bit slot containing no or two optical
pulses is equivalent to receiving a logical signal of the complementary logical
state.
It will be appreciated by a person skilled in the art that the gate
outputs 8,9 may be coupled to the switching input 10 of a second gate 6, to provide
a wavelength translation, if required. In this case, the second gate 6 will use
the optical pulses received from the respective output 8,9 of the first gate as
switching inputs such that the output from the second gate 6 is effectively a
regenerated copy of the output of the first gate 6. Such a setup is disclosed in
the co-pending application WO98/44512.
Figure 1d shows an optical pulse source 11, which usually takes the
form of a semiconductor laser producing pulses at a wavelength of approximately
1.5 micrometers. The pulse repetition rate is approximately 1GHz with the laser
providing 10ps pulses after linear chirp compensation in a length of non-dispersive
optical fibre, although pulse repetition rates of over 100GHz are possible. Such
a pulse source 11 will generally be configured to produce one of two optical pulse
sequences. The first configuration, which will hereinafter be called a pulse stream
generator generates an optical pulse stream with an optical pulse in every bit
slot. The second configuration, which will hereinafter be called a sync pulse generator,
generates an optical pulse stream with an optical pulse in one bit slot only.
An example of a binary adder according to the present invention is
shown in Figures 2 and 4, with Figure 2 showing schematically the configuration
of the components of the binary adder and Figure 4 showing schematically the configuration
of the logic gates of Figure 2. As shown, the adder comprises an input 12 which
supplies an optical pulse stream comprising two or more optical binary words in
sequence, each binary word being of L bit slots in length, to the adder circuit.
The input 12 is coupled to the first combiner input 14 of an optical
combiner 13, which has a combiner output 16 coupled to a gate switching input 18
of an optical gate 17. The gate 17 acts as an AND gate to generate, at its first
gate output 20, the logical AND of optical pulse streams received at the gate
switching input 18 and the gate input 19. In these circumstances, the gate inputs
can be considered as a first AND gate input 18 and a second AND gate input 19,
whilst the first gate output 20 is an AND gate output 20. The second gate output
21 is unused in this configuration.
The AND gate output 20 is coupled via an optical delay line 22 to
the second combiner input 15 of the combiner 13. Optical pulses traveling along
the delay line 22 will be delayed by L+1 bit slots.
The combiner output 16 is also coupled to a first XOR gate input
36 of an optical XOR gate 35. The XOR gate 35 comprises an optical combiner 23,
an optical non-linear gate 27 and a pulse stream generator 33 which generates a
stream of optical pulses.
The first combiner input 24 of the combiner 23 is connected to the
combiner output 16 via the first XOR gate input 36. The combiner output 26 is coupled
to the gate switching input 28 of the gate 27, whose gate input 29 is coupled
to the pulse stream generator 33 so as to receive the stream of optical pulses.
The second gate output 31 is unconnected, whilst the first gate output
30 is coupled via an XOR gate output 38 to a delay line 32, which introduces a
delay, for optical pulses traveling along its length, of a time interval equivalent
to L bit slots.
The use of an L bit slot delay and an L+1 bit slot delay allows the
optical words output from the XOR gate and the AND gate to be offset by one bit
slot with respect to each other. It is preferable to obtain a one bit slot offset
in this manner, as opposed to using alternative circuit configurations such as
a single one bit slot delay, as one bit slot delays are difficult to achieve at
high bit rates.
The delay line 32 is connected, via a second XOR gate input 37, to
the combiner input 25 and also to the second AND gate input 19 of the optical AND
gate 17.
As mentioned above, the optical gate 27, the pulse stream generator
33 and the optical combiner 23 in combination form an exclusive OR gate, as shown
in Figure 4, which operates as follows.
The optical combiner 23 combines any optical pulses received at the
combiner inputs 24, 25 such that if only a single optical pulse is received at
either input 24, 25 during any one bit slot, then the output from the combiner
will be a single optical pulse. This optical pulse then acts as a switching signal
causing the gate 27 to enter the switched state, which results in a single optical
pulse being transferred from the gate input 29 to the first gate output 30.
However, if a single optical pulse is received at both the combiner
inputs 24, 25, then the optical combiner 23 will output two optical pulses in the
same bit slot. As mentioned above, the gate switching input 22 detects a total
energy equivalent to two optical pulses, which does not act as a switching signal.
Accordingly, the gate remains in an unswitched state and the stream of optical
pulses from the pulse stream generator 33 will be transferred to the second gate
output 31. The gate also remains in the unswitched state if no optical pulses are
received by the optical combiner 23, during the respective bit slot.
Thus, the XOR gate 35 generates, at the XOR gate output 38, the XOR
of the optical pulses received at the XOR gate inputs 36, 37. An optical pulse
is output from the XOR gate output 30 when a single optical pulse only is received,
during a bit slot, by one of the two XOR gate inputs 36, 37. If none or two optical
pulses are received then no optical pulse is output.
In fact, with the delay line 32 added to feed back the output from
the XOR gate output 38 to the second XOR gate input 37, then an XOR gate is formed
which will generate the XOR of two L bit slot words supplied consecutively to
the XOR gate input 36.
Operation of the binary adder will now be described.
The first example to be described with reference to Table 1 and Figure
3 is the simple binary addition of two binary words, each of L bit slots in length,
where L=10.
In this case the binary numbers to be added are "0001101011" and
"1101000111", which gives a result of "1110110010".
Bit Slot
First Combiner Input
(14)
Second Combiner Input
(15)
First Gate Inputs
(18 & 36)
Second Gate Inputs
(19 & 37)
AND Gate Output
(20)
XOR Gate Output
(38)
1
1
0
1
0
0
1
2
1
0
1
0
0
1
3
0
0
0
0
0
0
4
1
0
1
0
0
1
5
0
0
0
0
0
0
6
1
0
1
0
0
1
7
1
0
1
0
0
1
8
0
0
0
0
0
0
9
0
0
0
0
0
0
10
0
0
0
0
0
0
11
1
0
1
1
1
0
12
1
0
1
1
1
0
13
1
0
1
0
0
1
14
0
0
0
1
0
1
15
0
0
0
0
0
0
16
0
0
0
1
0
1
17
1
0
1
1
1
0
18
0
0
0
0
0
0
19
1
0
1
0
0
1
20
1
0
1
0
0
1
21
0
0
0
0
0
0
22
0
1
1
0
0
1
23
0
1
1
1
1
0
24
0
0
0
1
0
1
25
0
0
0
0
0
0
26
0
0
0
1
0
1
27
0
0
0
0
0
0
28
0
1
1
0
0
1
29
0
0
0
1
0
1
30
0
0
0
1
0
1
31
0
0
0
0
0
0
32
0
0
0
1
0
1
33
0
0
0
0
0
0
34
0
1
1
1
1
0
35
0
0
0
0
0
0
36
0
0
0
1
0
1
37
0
0
0
0
0
0
38
0
0
0
1
0
1
39
0
0
0
1
0
1
40
0
0
0
1
0
1
41
0
0
0
0
0
0
42
0
0
0
1
0
1
43
0
0
0
0
0
0
44
0
0
0
0
0
0
45
0
1
1
0
0
1
46
0
0
0
1
0
1
47
0
0
0
0
0
0
48
0
0
0
1
0
1
49
0
0
0
1
0
1
50
0
0
0
1
0
1
51
0
0
0
0
0
0
52
0
0
0
1
0
1
53
0
0
0
0
0
0
54
0
0
0
0
0
0
55
0
0
0
1
0
0
56
0
0
0
1
0
1
57
0
0
0
0
0
0
58
0
0
0
1
0
1
59
0
0
0
1
0
1
60
0
0
0
1
0
1
The first binary word is transferred from the input 12 to the first
input 14 of the optical combiner 13, during bit slots 1-10. Initially there are
no other optical pulses present in the circuit. Consequently, the first word is
transferred via the combiner 13 to the AND gate 17, which generates an output containing
no optical pulses at the AND gate output 20, as shown in Figure 3 and Table 1.
The first word is also transferred to the XOR gate 35, which generates
a copy of the word at the XOR gate output 38. This is transferred to the delay
line 32, which introduces a time delay equivalent to L bit slots (i.e. 10 bit
slots), such that the word is transferred to the second AND gate input 19 and the
second XOR gate input 37 during bit slots 11-20.
Simultaneously, during bit slots 11-20, the second binary word is
transferred to the first combiner input 14. Again, with no optical pulses present
at the second combiner input 15, the second binary word is simply transferred
to the first AND gate input 18 and the first XOR gate input 36, as shown in Table
1 and Figure 3.
The XOR gate 35 generates at the output 38 an optical XOR word representing
the logical XOR combination of the firsc and second words. This is transferred
to the delay line 32 and, after being delayed by a time interval of L bit slots
(i.e. 10 bit slots), the optical XOR word is transferred to the second AND gate
input 19 and the second XOR gate input 37, during bit slots 21-30.
The AND gate 17 generates at the AND gate output 20 an optical AND
word representing the logical AND combination of the first and second words. This
is transferred to the delay line 22 and, after being delayed by a time interval
of L+1 bit slots (i.e. 11 bit slots), the optical AND word is transferred to the
second combiner input, during bit slots 22-31. With no further binary words being
transferred from the input 12, the optical AND word is transferred to the first
AND gate input 20 and the first XOR gate input 36, during bit slots 22-31.
Thus during bit slots 21-30, the XOR gate 35 and the AND gate 17
receive the optical XOR word generated during bit slots 11-20 and, by virtue of
the optical AND word being delayed by an additional bit slot, the optical AND
word generated in bit slots 10-19. From these optical words, further AND and XOR
optical words are generated and output from the AND and XOR gate outputs 38, 20,
respectively.
These further optical words are again delayed by the respective delay
lines 32, 22 and returned to the first and second AND and XOR gate inputs 18, 19,
36, 37.
This process is repeated until there are no optical pulses present
in the output from the AND gate 17, for an entire L bit slot duration, i.e. during
bit slots 41-50, as shown in Figure 3 and Table 1. At this time the optical XOR
word output from the XOR gate output 38 represents the binary sum of the first
and second words.
A second example of the present invention of a binary adder is shown
in Table 2. Again the binary numbers to be added are "0001101011" and "1101000111".
However, in this example the most significant bit if represented by the first
bit slot of the optical binary words. Accordingly, the delay line 22 of Figure
1 would be replaced by an L-1 bit slot delay line. Again the output obtained in
bit slots 41-50 represents the binary sum "1110110010".
Table 2 is therefore to be interpreted in a similar manner to Table
1 except that the optical AND word output from the AND gate output 20 is delayed
by a time interval corresponding to L-1 bit slots (i.e. 9 bit slots), as opposed
to L+1 bit slots, before being transferred to the second combiner input.
Bit Slot
First Combiner Input
(14)
Second Combiner Input
(15)
First Gate Inputs
(18 & 36)
Second Gate Inputs
(19 & 37)
AND Gate Output
(20)
XOR Gate Output
(38)
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
4
1
0
1
0
0
1
5
1
0
1
0
0
1
6
0
0
0
0
0
0
7
1
0
1
0
0
1
8
0
0
0
0
0
0
9
1
0
1
0
0
1
10
1
0
1
0
0
1
11
1
0
1
0
0
1
12
1
0
1
0
0
1
13
0
0
0
0
0
0
14
1
0
1
1
1
0
15
0
0
0
1
0
1
16
0
0
0
0
0
0
17
0
0
0
1
0
1
18
1
0
1
0
0
1
19
1
0
1
1
1
0
20
1
0
1
1
1
0
21
0
0
0
1
0
1
22
0
0
0
1
0
1
23
0
1
1
0
0
1
24
0
0
0
0
0
0
25
0
0
0
1
0
1
26
0
0
0
0
0
0
27
0
0
0
1
0
1
28
0
1
1
1
1
0
29
0
1
1
0
0
1
30
0
0
0
0
0
0
31
0
0
0
1
0
1
32
0
0
0
1
0
1
33
0
0
0
1
0
1
34
0
0
0
0
0
0
35
0
0
0
1
0
1
36
0
0
0
0
0
0
37
0
1
1
1
1
0
38
0
0
0
0
0
0
39
0
0
0
1
0
1
40
0
0
0
0
0
0
41
0
0
0
1
0
1
42
0
0
0
1
0
1
43
0
0
0
1
0
1
44
0
0
0
0
0
0
45
0
0
0
1
0
1
46
0
1
1
0
0
1
47
0
0
0
0
0
0
48
0
0
0
0
0
0
49
0
0
0
1
0
1
50
0
0
0
0
0
0
51
0
0
0
1
0
1
52
0
0
0
1
0
1
53
0
0
0
1
0
1
54
0
0
0
0
0
0
55
0
0
0
1
0
1
56
0
0
0
1
0
1
57
0
0
0
0
0
0
58
0
0
0
0
0
0
59
0
0
0
1
0
1
60
0
0
0
0
0
0
As shown in Figure 3, the optical word representing the binary sum
is repeatedly output from the XOR gate output until the circuit is reset. This
occurs as a result of the optical pulses forming the output from the XOR gate
output 38 being fed back to the second XOR gate input 37. With no additional optical
pulses present elsewhere in the circuit, any pulses fed back to the second XOR
gate input 37 will be regenerated by the XOR gate 35 and again output. Accordingly,
reset of the circuit is achieved by resetting the XOR gate 35.
In order to reset the XOR gate it is necessary to ensure that no
optical pulses are transferred from gate input 29 to the first gate output 30 upon
reception of a switching signal at the gate switching input 28. This condition
must be maintained for at least L bit slots in order to reset every bit slot of
an L bit slot optical word.
This can be achieved by replacing the stream of optical pulses, received
from the pulse stream generator 33, by a stream of optical bit slots containing
an optical bit slot window of R optical bit slots, each of the R bit slots containing
no optical pulses. Accordingly, upon reception of a switching signal by the gate
switching unit 28 of the gate 27, the respective empty bit slot contained in the
R bit slot window is transferred to the first gate output 30 to the XOR gate output
38. To ensure all the bit slots of the word are reset. R must be greater than or
equal to L.
Such an R bit slot window containing no optical pulses can be obtained
from a window generator described in our co-pending application published under
the number WO-9914649, and which will now be described with reference to Figures
5 and 6.
Figure 5 shows a resettable binary adder, which includes the binary
adder of Figure 2 coupled to a window generator which comprises a pulse pair generator
52 and a switching device 53.
The switching device 53 has an input port 54, to which is coupled
an pulse stream generator 55, two output ports 56,38 and a switching input port
57 which is coupled to the generator output 76 of the pulse pair generator 52.
The switching device itself consists of an all optical non-linear
gate 58 the first gate output 59 of which is coupled to the second combiner input
65 of an optical combiner 63, via a feedback loop. The feedback loop is formed
from a delay line 67, which, for the purposes of the window generator, introduces
a time delay equivalent to a single bit slot. Accordingly, an optical pulse transferred
through the delay line 67 will arrive at the second combiner input 65 of the optical
combiner 63 in the bit slot immediately following the bit slot it would have arrived
in if it had been traveling through a non-delaying connection.
The gate input 61, is coupled to the switching device input port
54 to receive the optical pulse stream generated by the pulse stream generator
55, whilst the gate switching input 62 is coupled to the combiner output 66 of
the optical combiner 63. The first combiner input 64 is connected to the switching
device switching input port 57, to receive optical pulses from the pulse pair generator
52.
The pulse pair generator 52 consists of an all optical combiner 70.
Connected to a first combiner input 71 of the optical combiner 70 is a sync pulse
generator 74, whilst connected to the second input 72 is a delay line 75. The
delay line 75, which is also coupled to the sync pulse generator 74, operates to
add a time delay equal to a number of bit slots R. The combiner output 73 of the
combiner 70, is connected via an output port 76 of the pulse pair generator 52
to the switching input port 57 of the switching device 53.
Operation of the window generator of Figure 5 will now be described
with reference to Figure 6 which shows bit slot time lines for several locations
around the window generator circuit. Each time line, which is split into a series
of bit slots, shows the presence of optical pulses at the respective points in
the circuit. A stream of pulses is represented by the continuous presence of a
pulse although it could equally be shown as a series of discrete pulses.
As described above, the switching device 53 is coupled to the pulse
stream generator 55 which supplies the optical pulse stream to the input port 54
of the switching device and hence to the gate input 61 of the gate 58.
Initially, with no optical pulse applied to the switching input port
57 of the switching device, there will be no optical pulse input to the gate switching
input 62 of the gate 58. Accordingly, the stream of optical pulses supplied to
the gate input 61 will pass through the all optical gate 58 to the gate output
60. As a result, no optical pulses are output from the gate output 59 and a stream
of pulses are output from the second gate output 60.
In bit slot 5, as labeled on Figure 6, the single optical pulse is
output from the sync pulse generator 74 and transferred to the optical combiner
70. As shown in Figure 6, the single optical pulse arrives at a point 77 and is
split into two copies, one of which is transferred directly to the first combiner
input 71 of the all optical combiner 70, whilst the other is transferred to the
second combiner input 72, via the delay line 75. The pulse traveling along the
delay line 75 will be delayed by R bit slots (in the present example R=10) with
respect to the pulse traveling directly to the optical combiner 70. As a consequence,
the optical combiner 70 will receive one optical pulse at the combiner input 71
in the bit slot 5 and a second optical pulse at combiner input 72 in bit slot
15, as shown in Figure 6.
These optical pulses are then combined to form a single optical pulse
stream including two optical pulses separated by R bit slots, which is transferred
to the switching input port 57 of the switching device 53.
When the first pulse is received from the pulse pair generator 52,
it will be input to the switching input port 57 of the switching device and hence
to the first combiner input 64 of the optical combiner 63, as shown. This optical
pulse is then transferred to the gate switching input 62 of the gate 58 to act
as a switching signal. This will cause a first optical pulse to be switched from
the gate input 61 to the gate output 59 during bit slot 5.
This optical pulse is fed back via the delay line 67 to the second
combiner input 65 of the optical combiner 63. Because the delay line 67 introduces
a single bit delay into the feedback loop, the fed back optical pulse will arrive
back at the gate switching input 62 in bit slot 6, as the subsequent optical pulse
output from the pulse stream generator 55 is received at the gate input 61. Accordingly
the first optical pulse output from the gate output 59 will act as a switching
signal, in bit slot 6, causing the next optical pulse to be switched from the gate
input 61 to the gate output 59. This is repeated for bit slots 6 to 14, causing
a stream of 50 optical pulses to be output from the gate output 59.
This continues until the second pulse is output from the pulse pair
generator 52, in bit slot 15. This pulse will arrive at the first combiner input
64 of the optical combiner 63 in bit slot 55, the same time as an optical pulse
from the feedback loop is received at the second combiner input 65.
With both pulses arriving at the all optical combiner 63 simultaneously,
two optical pulses will be output in the same bit slot. Accordingly, the gate switching
input 62 will detect a total energy equivalent to two optical pulses. This does
not act a switching signal and as a result, the stream of optical pulses from the
pulse stream generator 55 will no longer be switched to the gate output 59.
Consequently, when placed in combination, the optical combiner 63
and the gace 58 function as an XOR system, with the gate 58 only entering the switched
state when only one optical pulse is received at one of the optical combiner inputs
64, 65. When no pulse is received, or a pulse is received at both inputs, simultaneously
during the same bit slot period, then the signal output from the combiner will
not act as a switching signal, causing the gate to remain in an unswitched state.
Thus by providing an optical signal stream from the pulse pair generator
52 with two pulses, the pulses being separated by a predetermined number of bit
slots R, the window generator will output an optical signal stream consisting
of K optical pulses, from the gate output 59.
Furthermore, as it is the delay line 75 that introduces the delay
in the pulse pair generator 52, it is the length of the time delay of the delay
line 75 that sets the number of bits R. Thus in the example of Figure 6, the delay
line 75 introduces a delay equivalent to 10 bit slots, causing the window generator
to output a sequence of 50 optical pulses from the output port 56. However, the
number of bit slots that the delay line 75 delays the optical pulse by could be
altered, causing a corresponding change in the number of optical pulses output
from the output port 56 of the switching device 53.
The second gate output 50 generates an optical signal stream that
is the logical complement of the optical signal stream generated by the first gate
output 59. The second output port 78 is therefore coupled to the gate output 60
so as to produce an optical signal stream including an R bit slot window, the
R bit slots not having an optical pulse in, with any bit slots not inside the R
bit window including an optical pulse.
In order for reset of the binary adder to occur, the output port
78 of the window generator is connected to the gate input 29 of the gate 27 of
the XOR gate 35', which is similar to the XOR gate 35 of Figure 2, lacking only
the pulse stream generator 33.
The window generator then operates to generate a stream of optical
bit slots containing optical pulses allowing the adder to be used as normal. Then,
as reset of the adder is required the window generator generates an R optical
bit slot window containing no optical bit slots, causing R of the optical bit slots
of the output from the XOR gate 35' to be reset. Accordingly, for R>L, the adder
is completely reset such that the circuit no longer contains any optical pulses.
The third example of operation of the binary adder of Figure 2 will
now be described with reference to Table 3 and Figure 7. This is the operation
of the circuit as a simple counting circuit.
In order to operate as a counter, the circuit must be supplied with
a sequence of binary words, each word being of L bit slots in length and containing
only single optical pulse which in this example is in the first bit slot. The
adder circuit will effectively output a binary value, at the XOR gate output 38,
representing the number of words of this format which have been received.
In the present example, shown in Figure 7 and Table 3, the input
12 supplies a sequence of four six bit slot length words (i.e. L=6), each word
having a single optical pulse in the first bit slot, to the first combiner input
14.
When the first binary word is transferred from the input 12 to the
first input 14 of the optical combiner 14, during bit slots 1-6, there are no other
optical pulses present in the circuit. Consequently, the first word is transferred
via the combiner 13 to the AND gate 17, which generates an output containing no
optical pulses at the AND gate output 20, as shown in Figure 7 and Table 3.
Bit Slot
First Combiner Input
(14)
Second Combiner Input
(15)
First Gate Inputs
(18 & 36)
Second Gate Inputs
(19 & 37)
AND Gate Output
(20)
XOR Gate Output
(38)
1
1
0
1
0
0
1
2
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
6
0
0
0
0
0
0
7
1
0
1
1
1
0
8
0
0
0
0
0
0
9
0
0
0
0
0
0
10
0
0
0
0
0
0
11
0
0
0
0
0
0
12
0
0
0
0
0
0
13
1
0
1
0
0
1
14
0
1
1
0
0
1
15
0
0
0
0
0
0
16
0
0
0
0
0
0
17
0
0
0
0
0
0
18
0
0
0
0
0
0
19
1
0
1
1
1
0
20
0
0
0
1
0
1
21
0
0
0
0
0
0
22
0
0
0
0
0
0
23
0
0
0
0
0
0
24
0
0
0
0
0
0
25
0
0
0
0
0
0
26
0
1
1
1
1
0
27
0
0
0
0
0
0
28
0
0
0
0
0
0
29
0
0
0
0
0
0
30
0
0
0
0
0
0
31
0
0
0
0
0
0
32
0
0
0
0
0
0
33
0
1
1
0
0
1
34
0
0
0
0
0
0
35
0
0
0
0
0
0
36
0
0
0
0
0
0
37
0
0
0
0
0
0
38
0
0
0
0
0
0
39
0
0
0
1
0
1
40
0
0
0
0
0
0
41
0
0
0
0
0
0
42
0
0
0
0
0
0
43
0
0
0
0
0
0
44
0
0
0
0
0
0
45
0
0
0
1
0
1
46
0
0
0
0
0
0
47
0
0
0
0
0
0
48
0
0
0
0
0
0
49
0
0
0
0
0
0
50
0
0
0
0
0
0
51
0
0
0
1
0
1
52
0
0
0
0
0
0
53
0
0
0
0
0
0
54
0
0
0
0
0
0
55
0
0
0
0
0
0
56
0
0
0
0
0
0
57
0
0
0
1
0
1
58
0
0
0
0
0
0
59
0
0
0
0
0
0
60
0
0
0
0
0
0
The first word is also transferred to the XOR gate 35, which generates
a copy of the word at the XOR gate output 38. This is transferred to the delay
line 32, which introduces a time delay equivalent to L bit slots (i.e. 6 bit slots),
such that the word is transferred to the second AND gate input 19 and the second
XOR gate input 37 during bit slots 7-12.
Simultaneously, during bit slots 7-12, the second binary word is
transferred to the first combiner input 14. Again, with no optical pulses present
at the second combiner input 15, the second binary word is simply transferred
to the first AND gate input 18 and the first XOR gate input 36, as shown in Table
3 and Figure 7.
The XOR gate 35 generates an optical XOR word representing the logical
XOR combination of the first and second words at the output 38, which contains
no optical pulses.
Simultaneously, the AND gate 17 generates an optical AND word representing
the logical AND combination of the first and second words at the AND gate output
20. This is transferred to the delay line 22 and, after being delayed by a time
interval of L+1 bit slots (i.e. 7 bit slots), the optical AND word is transferred
to the second combiner input, during bit slots 14-19.
The third binary word is received at the first input 14 of the combiner
13 during bit slots 13-18 and combined with the optical AND word generated during
bit slots 6-11, to generate a combination optical word. This combination optical
word, shown in Table 3, is transferred to the first gate inputs 18, 36 of the AND
gate 17 and the XOR gate 35, during bit slots 13-18.
The second gate inputs 19, 37 have no optical pulses supplied at
this time by virtue of the optical XOR word generated during bit slot 7-12 having
no optical pulses.
Accordingly, the XOR gate 35 generates an optical XOR word, which,
as there are no optical pulses present at the second XOR gate input 37, is a copy
of the combination optical word. This optical XOR word is transferred to the delay
line 32 and, after being delayed by a time interval of L bit slots (i.e. 6 bit
slots), is transferred to the second AND gate input 19 and the second XOR gate
input 37, during bit slots 19-24.
The AND gate generates an optical AND word containing no optical
pulses. Consequently, there are no optical pulses present at the second combiner
input 15, during bit slots 19-24, when the fourth binary word is received by the
first combiner input 14 and the fourth binary word is transferred to the first
gate outputs 18, 36.
Thus during bit slots 19-24, the XOR gate 35 and the AND gate 17
receive the optical XOR word generated during bit slots 13-18, and, the fourth
binary word. From these, further AND and XOR optical words are generated and output
from the AND and XOR gate outputs 38, 20, respectively.
These further words are again delayed by the respective delay lines
32, 22 and returned to the first and second AND and XOR gate inputs 18, 19, 36,
37.
with no further binary words being transferred from the input 12,
the optical AND word is transferred to the first AND gate input 20 and the first
XOR gate input 36, during bit slots 26-31. Meanwhile, the optical XOR word is
transferred to the second gate inputs 19, 37, during bit slots 25-30.
This process is repeated until there are no optical pulses present
at the output 20 of the AND gate 17, for an entire L bit slot duration, i.e. the
optical AND word contains no optical pulses as shown during bit slots 31-36, in
Figure 7 and Table 3. At this time the optical XOR word output from the XOR gate
output 38 is an optical binary word with a binary value "100", representing the
decimal value "4". Thus the circuit counts the number of incoming binary words,
as long as the binary words have the required format.
It should be noted that in the current example, the maximum binary
value that can be counted is "111111" (i.e. decimal value "63"). This limitation
is imposed by virtue of the binary words having only 6 bit slots. Thus, by increasing
the number of bit slots, the maximum value that can be counted increases. Expressed
mathematically, the maximum decimal value to which the circuit can count is (2L-1),
where L is the number of optical bit slots in the optical binary words.
A forth example of the operation of the binary adder of Figure 2
is shown in Table 4. In this case the circuit again operates as a simple counter
with a single optical pulse in the last bit slot of the input optical binary words.
Accordingly, the delay line 22 of Figure 2 would be replaced by an L-1 bit slot
delay.
Table 4 is to be interpreted in a similar manner to Table 3, except
that the AND word output from the AND gate output 20 is delayed by L-1 bit slots
(i.e. 5 bit slots) before being transferred to the second combiner input. Accordingly,
operation in accordance with Table 4 will not be described in detail.
Again reset of the circuit may be achieved by the use of an optical
bit slot window, each of the optical bit slots containing no optical pulse, in
a similar manner to that described with reference to Figures 5 and 6.
A second embodiment of the present invention is shown in schematic
form in Figure 8 which shows a schematic representation of the configuration of
the logic gates used for this alternative design. Components in Figure 8 identical
to those in Figure 4 are indicted by equivalent reference numerals except increased
by 100.
Bit Slot
First Combiner Input (14)
Second Combiner Input (15)
First Gate Inputs (18 & 36)
Second Gate Inputs (19 & 37)
AND Gate Output (20)
XOR Gate Output (38)
1
0
0
0
0
0
0
2
0
0
0
0
0
0
3
0
0
0
0
0
0
4
0
0
0
0
0
0
5
0
0
0
0
0
0
6
1
0
1
0
0
1
7
0
0
0
0
0
0
8
0
0
0
0
0
0
9
0
0
0
0
0
0
10
0
0
0
0
0
0
11
0
0
0
0
0
0
12
1
0
1
1
1
0
13
0
0
0
0
0
0
14
0
0
0
0
0
0
15
0
0
0
0
0
0
16
0
0
0
0
0
0
17
0
1
1
0
0
1
18
1
0
1
0
0
1
19
0
0
0
0
0
0
20
0
0
0
0
0
0
21
0
0
0
0
0
0
22
0
0
0
0
0
0
23
0
0
0
1
0
1
24
1
0
1
1
1
0
25
0
0 0
0
0
0
0
26
0
0
0
0
0
0
27
0
0
0
0
0
0
28
0
0
0
0
0
0
29
0
1
1
1
1
0
30
0
0
0
0
0
0
31
0
0
0
0
0
0
32
0
0
0
0
0
0
33
0
0
0
0
0
0
34
0
1
1
0
0
1
35
0
0
0
0
0
0
36
0
0
0
0
0
0
37
0
0
0
0
0
0
38
0
0
0
0
0
0
39
0
0
0
0
0
0
40
0
0
0
1
0
1
41
0
0
0
0
0
0
42
0
0
0
0
0
0
43
0
0
0
0
0
0
44
0
0
0
0
0
0
45
0
0
0
0
0
0
46
0
0
0
1
0
1
47
0
0
0
0
0
0
48
0
0
0
0
0
0
49
0
0
0
0
0
0
50
0
0
0
0
0
0
51
0
0
0
0
0
0
52
0
0
0
1
0
1
53
0
0
0
0
0
0
54
0
0
0
0
0
0
55
0
0
0
0
0
0
56
0
0
0
0
0
0
57
0
0
0
0
0
0
58
0
0
0
1
0
1
59
0
0
0
0
0
0
60
0
0
0
0
0
0
As shown in Figure 8, the adder comprises an AND gate 117 and an
XOR gate 135. The AND gate output 120 is coupled via a delay line 122, that introduces
a L+1 bit slot delay, to the first AND gate input 118 and the first XOR gate input
136. The XOR gate output 138 is coupled via a delay line 122, that introduces an
L bit slot delay, to the second AND gate input 119 and the second XOR gate input
137. An input 112, which supplies the words to be added is coupled to the first
AND gate input 118 and the first XOR gate input 136.
Comparison of Figures 4 and 8 shows that Figure 8 is similar to the
apparatus of Figure 4 with the optical combiner 13 removed. Examination of the
optical pulses in Figure 3 shows that the optical combiner 13 is not actually
required to combine any optical pulses during this operation, primarily due to
there being no optical pulses received by the combiner input 14 after the second
binary word is supplied. Accordingly, it is possible for the adder to function
without a combiner 13 as long as only two binary words are supplied to the combiner
input 14.
Accordingly, Figure 8 shows an example of a suitable apparatus configuration
that could be used as an adder for adding two binary numbers as in the example
described with respect to Table 1 and Figure 3.
As will be appreciated, if the delay line 122 is replaced by an L-1
bit slot delay line, the apparatus of Figure 8 can be used as a binary adder in
a similar manner to the example set out in Table 2.
Figure 9 shows a schematic representation of the configuration of
the logic gates used in a binary adder according to a third embodiment of the present
invention.
In this embodiment of the present invention, the use of feedback
to repeatedly generate the optical XOR word and the optical AND word is replaced
by a sequence of optical AND gate and XOR gate pairs 201, 202, 203, 204.
As each pair 201, 202, 203, 204 is identical and therefore only one
will be described with reference to Figure 9. The AND/XOR pair 201 comprises an
AND gate 217 and an XOR gate 235. The first gate inputs 218, 236 of the AND gate
217 and the XOR gate 235 are connected together and to a first word input port
210 which receives the first word to be added. The Second gate inputs 219, 237
of the AND gate 217 and the XOR gate 235 are also connected together and to a
second word input port 210 which receives the second word to be added.
The AND gate output 220 is coupled via a delay line 222, which introduces
a M+1 bit slot delay, to an output port 212, whilst the XOR gate output 238 is
coupled via a delay line 232, which introduces an M bit slot delay, to an output
port 212.
Each AND/XOR pair will operate on first and second binary words received
at the first and second input ports 210, 211 simultaneously, to generate an optical
word representing the logical AND at the AND gate output 220 and an optical word
representing the logical XOR at the XOR gate output 238. Transfer of the optical
AND word and the optical XOR word, to the respective first and second output ports
212, 213, is delayed by M+1 and M bit slots respectively, such that the optical
AND word is delayed by one additional bit slot with respect to the optical XOR
word. The words are then output to the respective first and second input ports
210, 211 of the next AND/XOR gate pair 202.
The apparatus therefore functions as for the apparatus of Figure
8, with the process of feedback being replaced by transfer to a subsequent AND/XOR
gate pair. By ensuring that a sufficient number of AND/XOR gate pairs are provided
in sequence, the AND gate output will eventually contain no optical pulses, in
which case the optical XOR word generated by the respective XOR gate is the binary
sum of the first and second words. The number of required AND/XOR gates cannot
however be predetermined and this design does therefore require a sufficient AND/XOR
gate pairs for the correct answer to be generated. However, by monitoring the
optical AND word output from each AND/XOR gate pair, it is possible to determine
which AND/XOR gate pair generates an optical XOR word representing the binary sum
of the first and second words.
With no feedback loop, resetting of the apparatus is automatic, with
no optical pulses remaining in the circuit once the result is generated. Furthermore
as the requirement for the delay lines is only that the delay lines must delay
the output words such that the optical AND word is offset by one bit slot with
respect to the XOR word, then the total length of delay time may be reduced.
Thus, for example, if the circuit of Figure 2 is used, for a large
number of bit slots L, the transfer of words is delayed by L bit slots per feedback.
However in the design of Figure 9 the transfer is only delayed by M bit slots
where, M can be controlled such that M « L, thereby reducing the processing time.
It is however preferable to maintain a value of M>1 as single
bit delays are difficult to achieve at high bit rates. Therefore by using a M+1
bit slot delay and an M bit slot delay, a relative offset of one bit slot can be
conveniently achieved.
Again, an M-1 bit slot delay could be used instead of the M+1 bit
slot delay if the correct format of binary word is used.
An alternative possibility is to couple a sequence of the optical
AND/XOR gate pairs described in the third embodiment of the present invention,
to a feedback system of the first embodiment of the present invention. This would
enable the system co begin summing two binary words in the sequence of AND/XOR
gate pairs whilst a previous calculation is being completed by the feedback system
according to the first embodiment. Furthermore the number of AND/XOR gate pairs
can be reduced whilst still enabling the binary sum of the first and second, optical
words to be determined.