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Computer organization Notes-Half Adder

The most basic digital arithmetic circuit is the addition of two binary digits. A combinational circuit that performs the arithmetic addition of two bits is called a half adder. Half adder is a combinational logic circuit with two inputs and two outputs. The input variables of a half adder are called the augend and addend bits. The output variables are called as sum and carry. It is necessary to specify two output variables because the sum of 1 +1 is binary 10, which has two digits. We assign symbols A and B to the two input variables and S (for sum) and C (for carry) to the two output variables. The block diagram for Half Adder is

The truth table for Half Adder is

The Circuit Diagram for Half Adder is

The C output is zero unless both inputs are 1. The S output represents the least significant bit of the sum. The Boolean functions for the two outputs can be obtained directly from the truth table :
S = A’B + AB’ = A⊕ B.
C = AB
The logic diagram is also drawn above. It consists of an exclusive-OR gate and an AND gate.

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