Design Procedure for Combinational Circuits

Design Procedure

• The design of combinational circuits starts from the outline of the problem statement and ends in a logic circuit diagram or a set of Boolean functions from which the logic diagram can be easily obtained. The design procedure of the combinational circuit involves following steps :

1. The problem definition.

2. The determination of number of available input variables and required output variables.

3.Assigning letter symbols to input and output variables.

4. The derivation of truth table indicating the relationships between input and output variables.

5. Obtain simplified Boolean expression for each output.

6. Obtain the logic diagram.

Example for Understanding

Example: 1

Design a combination logic circuit with three input variables that will produce a logic 1 output when more than one input variables are logic 1.

Solution :

Step 1: Derive the truth table for given statement.

Given problem specifies that there are three input variables and one output variable. We assign A, B and C letter symbols to three input variables and assign Y letter symbol to one output variable. The relationship between input variables and output variable can be tabulated as shown in truth Table 4.2.1.

Step 2 : Obtain simplified Boolean expression.

Now we obtain the simplified Boolean expression for output variable Y using K–map simplification.

Y = AC + BC + AB

Step 3 : Draw logic diagram.

In this chapter we are going to study various combinational circuits using above illustrated design method.

Examples with Solutions

Example: 2

A majority gate is a digital circuit whose output is equal to 1 if the majority of inputs are 1's. The output is 0 otherwise. Using a truth table, find the Boolean function implemented by a 3–input majority gate. Simplify the function and implement with gates.

Solution :

Y = BC + AB+ AC

Implementation after simplification

Example: 3

Design a circuit that has one control line C and three data lines D₁, D₂, D₃. When the control line is high, the circuit is to detect when one of the data lines has a 1 on it. No more than one data line will ever have a 1 on it. When the control line is low, the circuit will output a 0, regardless of what is on the data lines.

Solution : The truth table for the given problem is as shown below.

Y = CD₃ + CD₂ + CD₁

K–map simplification

Logic diagram

Review Question

1. Explain the design procedure for combinational circuits.