Half Adder, Truth Table, Logical Expression, Implementation: (circuit diagram)

Half Adder (HA):

The simplest adder circuit is the half adder. A combinational arithmetic circuit known as a halfadder adds two numbers and outputs both a sum bit (s) and a carry bit (c). A combination circuit known as a half adder is used to add two bits. The output variables are sum and carry bits, and the input variables are augend and addend bits. The input bits are A and B.

Consider the following two input bits: A and B. Sum bit (s) is the X-OR of A and B. A halfadder operation makes clear that one X-OR gate and one AND gate are necessary for its construction.

A halfadder is used to add two single-digit binary numbers and results into a two-digit output. It is named as such because putting two halfadders together with the use of an OR gate results in a full adder. In other words, it only does half the work of a full adders.

The adder functions by combining the functions of fundamental logic gates; the most basic version only uses an XOR and an AND gate. Additionally, this can be changed into a circuit with only AND, OR, and NOT gates. This is especially helpful because the three simpler logic gate ICs (integrated circuits) are more widely used and accessible than the XOR IC. However, using three different chips rather than just one may result in a larger circuit.

Half Adder Truth Table

Here we perform two operations Sum and Carry, thus we need two K-maps one for each to derive the expression.

Logical Expression

For Sum 

Sum = A XOR B

For Carry

Carry = A AND B 

Implementation: (circuit diagram)

Note: When performing multi addition, the half adder two inputs are the only ones available, and it is not possible to add a carry from the lower order bits.