Combinational logic circuits and Sequential logic circuits

COMBINATIONAL LOGIC CIRCUITS AND SEQUENTIAL LOGIC CIRCUITS

Basically the digital circuits are one of the following types:

(a) Combinational logic circuits

(b) Sequential logic circuits

A combinational logic circuit is defined as a logic circuit the output of which depends only upon the combination of the inputs. The output does not depend on the past inputs or past outputs. Thus combinational circuits do not have memory elements.

Examples: Adder, subtractors, multiplexers and comparators etc.,

In case of a sequential logic circuit, the output of which depends upon the present time, the previous output and the sequence in which input are applied. Sequential circuit requires a memory element. Examples: Flip-flops

1. Half Adder

Half Adder is a combinational circuit that performs the addition of two bits. This circuit needs two binary inputs and two binary outputs. The two binary outputs are sum and carry.

The simplified Boolean function from the truth table:

Limitations:

● In multi-digit addition we have to add two bits along with the carry of previous digit addition. This addition is not possible here.

● Half-adders are not to be used in practice.

2. Full Adder

● Full adder is a combinational circuit that forms the arithmetic sum of three input bits.

● It contains three inputs and two outputs (sum and carry).

Truth table for full adder.

K-Map for carry

Full adder using 2 half adder:

Figure 4.22 shows that a full adder can be implemented using two half adders and an OR gate.

The expression for sum output can be written as

This expression is same as that obtained for a full adder. 

Now, we write the expression for carry output C0 as

Thus the above expression is same that for a full adder. Therefore, we have showed that circuit in figure 4.22 really acts as a full adder.