This has 3 inputs- 2 are the numbers to be subtracted and c is the borrow which is taken for previous bit and we have 2 outputs Difference and the Borrow. The following table shows the results for all combinations of inputs:
a b c B(borrow) D(difference)= D = a – b – c
0 0 0 0 0
0 1 0 1 1
1 0 0 0 1
1 1 0 0 0
0 0 1 1 1
0 1 1 1 0
1 0 1 0 0
1 1 1 1 1
So we can get the equations for the D and B from the K-maps as shown on next page.
K-map for the output variable Difference is as follow:
We need 3 gate delays (3Δ) to get the output.
K-map for the variable Borrow is as follow:
Note that we have taken opposite values of variable a in the K-map.
We can get the output in 2 gate delays as we assume that a, b the input numbers are stored in flipflops hence we can have the complimented a from the flipflop directly. So we don’t consider the delay of the inverter shown in the circuit.
Similar to the adder we have D = ab’c’ + a’b’c + a’bc’ + abc = a xor b xor c
And B= a’b + a’c + bc
And we have the following circuit diagram for full subtractor:
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