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K. Mukherjee et al.
Table 1 Truth table of frequency-encoded half adder
Input
Output (Y )
A
B
SUM = A ⊕ B
CARRY = AB
υ 1 (0)
υ 1 (0)
υ 1 (0)
υ 1 (0)
υ 1 (0)
υ 2 (1)
υ 2 (1)
υ 1 (0)
υ 2 (1)
υ 1 (0)
υ 2 (1)
υ 1 (0)
υ 2 (1)
υ 2 (1)
υ 1 (0)
υ 2 (1)
no signal is present at the port 2 of the TOAD. Therefore, the output of the gate is
signal at frequency υ 1 . When input A is a signal at frequency υ 1 or υ 2 and input B
is a signal of frequency υ 2 or υ 1 , small portion of signals through the υ 1 pass filter
makes the control input of the TOAD at υ 1 and other portion of the signal passes
through the beam splitter makes the output of the TOAD is signal of frequency υ 1 .
At this condition, there is no signal present of the port 2 of the TOAD. Therefore, the
output of this TOAD is at υ 1 . When both the input A and B are signal at frequencies
υ 2 , there is no control signal receives of TOAD; hence, the data signal of frequency
υ 2 comes out from port 2 of the TOAD making final output at frequency υ 2 .
5 Frequency-Encoded Half Adder
Half adder is a device which can add two binary digit at a time and generates
‘SUM’ and ‘CARRY’ and for we use the XOR gate and AND gate described
above (Table 1).
6 Frequency-Encoded Half Subtractor
Half Subtractor is a device which can subtract two binary digit at a time generates
‘Difference’ and Operation of ‘Borrow’ generation:
Case (1): When A is at frequency υ 1, signal through the υ 1 pass filter makes the
control input of the TOAD T 1 is υ 1. In this condition, the control signal of the TOAD
T 1 forces the data signal of frequency υ 2 to be transmitted through the port 1 of the
TOAD T 1 and output of the TOAD T 1 is υ 2 and input B is a signal of frequency υ 1,
the small portion of signals through the υ 1 pass filter makes the control input of the
TOAD T 3 is υ 1 and other portion of the signal from beam splitter makes the output
of the TOAD T 3 at frequency υ 1. At this condition, there is no signal present of the
port 2 of the TOAD T 3 . Thus, the output of the TOAD T 3 is at frequency υ 1 , i.e.,
‘LOW’.
Case (2): If A is at frequency υ 1, the signal through the υ 1 pass filter makes the
control input of the TOAD T 1 is υ 1. In this condition, the control signal of the TOAD
K. Mukherjee et al.
Table 1 Truth table of frequency-encoded half adder
Input
Output (Y )
A
B
SUM = A ⊕ B
CARRY = AB
υ 1 (0)
υ 1 (0)
υ 1 (0)
υ 1 (0)
υ 1 (0)
υ 2 (1)
υ 2 (1)
υ 1 (0)
υ 2 (1)
υ 1 (0)
υ 2 (1)
υ 1 (0)
υ 2 (1)
υ 2 (1)
υ 1 (0)
υ 2 (1)
no signal is present at the port 2 of the TOAD. Therefore, the output of the gate is
signal at frequency υ 1 . When input A is a signal at frequency υ 1 or υ 2 and input B
is a signal of frequency υ 2 or υ 1 , small portion of signals through the υ 1 pass filter
makes the control input of the TOAD at υ 1 and other portion of the signal passes
through the beam splitter makes the output of the TOAD is signal of frequency υ 1 .
At this condition, there is no signal present of the port 2 of the TOAD. Therefore, the
output of this TOAD is at υ 1 . When both the input A and B are signal at frequencies
υ 2 , there is no control signal receives of TOAD; hence, the data signal of frequency
υ 2 comes out from port 2 of the TOAD making final output at frequency υ 2 .
5 Frequency-Encoded Half Adder
Half adder is a device which can add two binary digit at a time and generates
‘SUM’ and ‘CARRY’ and for we use the XOR gate and AND gate described
above (Table 1).
6 Frequency-Encoded Half Subtractor
Half Subtractor is a device which can subtract two binary digit at a time generates
‘Difference’ and Operation of ‘Borrow’ generation:
Case (1): When A is at frequency υ 1, signal through the υ 1 pass filter makes the
control input of the TOAD T 1 is υ 1. In this condition, the control signal of the TOAD
T 1 forces the data signal of frequency υ 2 to be transmitted through the port 1 of the
TOAD T 1 and output of the TOAD T 1 is υ 2 and input B is a signal of frequency υ 1,
the small portion of signals through the υ 1 pass filter makes the control input of the
TOAD T 3 is υ 1 and other portion of the signal from beam splitter makes the output
of the TOAD T 3 at frequency υ 1. At this condition, there is no signal present of the
port 2 of the TOAD T 3 . Thus, the output of the TOAD T 3 is at frequency υ 1 , i.e.,
‘LOW’.
Case (2): If A is at frequency υ 1, the signal through the υ 1 pass filter makes the
control input of the TOAD T 1 is υ 1. In this condition, the control signal of the TOAD