## Combinational Circuits

A combinational circuit is a connected arrangement of logic gates with a set of inputs and outputs. At any given time, the binary values of the outputs are a function of the binary combination of the input. The n binary input variables come from an external source, the m binary output variables go to an external destination and there is an interconnection of logic gates in between.

A combinational circuit transfer binary information from the given input data. A combinational circuit that performs the arithmetic addition of two bits is called a half-adder. One that performs the addition of three bits is called a full-adder. The name of the former stems from the fact that two half adder are needed to implement a full-adder. A block diagram of combinational circuit is shown in Fig.

 Block diagram of Combinational circuit

A combinational circuit can be described by a truth table showing the binary relationship between the n input variables and m output variable. The truth table list the corresponding output binary values for each of the 2input combinations.

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. The output of the exclusive-OR gate is called the SUM, while the output of the AND gate is the carry. The AND gate produces a high output only when both inputs are high. The exclusive-OR gate produces a high output if either input, but not both, is high.

The input variables of a half-adder are called the augend and addend bits. The output variables the sum and carry. When we add 1 and 1, we get sum=0 and carry=1. The logic diagram is shown in Fig. It consists of an exclusive-OR gate and an AND gate.

A full-Adder is a combinational circuit that forms the arithmetic sum of three input bits. One that performs the addition of three bits is called a full-adder. It consists of three input and two outputs. Two outputs are necessary because the arithmetic sum of three binary digits ranges in value from 0 to 3, and binary 2 or 3 require two digits. When all inputs bits are 0, the output is 0. The S output is equal to 1 when only 1 input is equal to one or when all three inputs are equal to 1. The C output has a carry of 1 if two or three inputs are equal to 1. The logic diagram of Full-Adder is shown in Fig.