Combination Circuits

Half Subtractors

Similar to the adder, we can also design subtractors and we also have half and full subtractors.

Half subtractor (HS): This circuit subtracts two bits and gives Borrow and Difference as 2 outputs. The following table shows the result for different combinations of inputs:

a              b            B(borrow)           D(difference)= D = a – b

0              0              0                              0

1              0              0                             1

0              1             1                              1

1              1              0                              0

We scan easily see that diference is 1 only when we have one of the inputs as 1 and other as 0 just like a XOR gate. So equation for difference is D= a’b + ab’

We can also obtain the equations using K-maps

And the digital circuit to implement the above functions is as follow:

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