## Computer organization Notes

Half Subtractors
Half-subtractor is a combinational circuit that is used to subtract two bits. Half subtractor is a combination circuit with two inputs and two outputs (difference and borrow). It produces the difference between the two binary bits at the input and also produces an output (Borrow) to indicate if a 1 has been borrowed. The block diagram for Half subtractor can be drawn as follows:

This circuit takes A and B as two inputs for the operation A-B. In the subtraction (A-B), A is called as Minuend bit and B is called as Subtrahend bit. The Outputs are Bout and D, where D signifies the difference between the two and Bout signifies the borrow from the next higher bit.
e.g. if A ≥ B then there is no need of Borrow and the value of B bit will be 0, however, when A < B then we have to take borrow and the value of B will be 1. This can be shown in truth table.

The truth table for Half Subtractor is

The Circuit Diagram for Half Subtractor is

From the above truth table , we can generate functions for the outputs Borrow Bout and Difference D as follows
Bout = A’B and D = A’B + AB’
These functions are already in simplified form so, no further solution is possible. Logical diagram for half subtractor can be drawn as follows:

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