# Subtractors

Subtraction can be done using various methods like direct subtraction of the corresponding bits or using complement’s methods as has already been discussed. If we use complement’s methods, subtraction is done using addition operation only and hence an adder can used to perform subtraction. However, we can design our own subtractors as we have done in case of adders. Same steps can be followed for designing of subtractors also.

Contents

## Half Subtractor

Half subtractor is a combinational circuit that is used to subtract two bits. This circuit takes A and B as two input for operation A-B. The outputs are A and D, where D signifies the difference between the two and B signifies the Borrow from the next higher bit.

### Block Diagram of half Subtractor

### Truth Table of Half Subtractor

### Logical Diagram of half Subtractor

## Full Subtractor

A full subtractor, just like full adder, takes into consideration that 1 might have been borrowed by the lower significant bit from the current bit. Hence, this circuit will have three inputs A, B and C, where C is precious borrow and A is the bit from which B will be subtracted. Outputs are represented, by B OUT and D.

### Block Diagram of Full Subtractor

### Truth Table of Full Subtractor

From the above Truth Table , we can device the function for both the output variables as –

B OUT = A’B’C + A’BC + ABC

D = A’B’C + AB’C’ + ABC

These expressions can be simplified using k-maps as follows –

### K-MAP

Simplified functions are represented as –

B OUT = A’ B + A ‘C + A B

D = A’ B’ C + A’ B ‘C + A B’ ‘C + ABC