Sub-Tractor

SUB-TRACTOR

Half Subtractor

The half-subtractor is a combinational circuit which is used to perform subtraction of two input (A & B) and two outputs (D & B_out). The logic symbol for a half-subtractor is show in figure 4.21 (a). The truth for half-subtractor is shown in table from the truth table it is clear that the difference output is 0 if A = B and 1 if A≠B, the borrow output B_out is 1 whenever A < B. If A is less than B, then subtraction is done by borrowing 1 from the next higher order bit.

From table, the Boolean expression for difference D and Barrow out B_out be written as follows

From the above equation, the half-subtractor can be implemented using an EX - OR gate, a NOT gate and AND gate as shown in figure 4.21(b).

Full-Subtractor

A full-subtractor is a combinational circuit that performs subtraction involving three bits inputs (A, B, B.) and two outputs (D and B_out). The truth table for the full-subtractor is given in table 4.29. The full-subtractor can be implemented using two half-subtractors and an OR gate as shown in figure 4.22.

From the table the sum of product expression for the difference (D) output can be written as