# How to Design Combinational Circuits From Specifications

Instructor: Lyna Griffin

Lyna has tutored undergraduate Information Management Systems and Database Development. She has a Bachelor's degree in Electrical Engineering and a Masters degree in Information Technology.

In this lesson we will design a combinational circuit. We will understand the problem definition, create a truth table and implement it in a design circuit.

## What Are Combinational Circuits?

Combinational circuits are electronic digital circuits with N number of inputs and M number of outputs using logic gates. They have no memory function and their present state is not affected in any way by the previous state. The state of the combinational circuit is completely dependent on the circuit inputs at the time: logic states 0 and 1.

A representation of a logic circuit is shown in Figure 1.

## Problem Definition

In this lesson, we will design a combinational circuit for a light switch in which the light bulb comes on anytime there is an input of a prime number between 0 and 10 in the circuit (a prime number being any number that is divisible only by itself and 1).

## The Basics

Since we are dealing with a logic circuit, we have to translate our desired input values stated in the problem definition into binary (zeros and ones). This means we are going to list our input values showing the corresponding desired equivalent in a binary table. With the given inputs, the light switch on state has an output value of logic 1 and the light switch off state has an output value logic 0.

The prime numbers between 0 and 10 are 2, 3, 5 and 7. This means from our problem definition the light switch in our combinational circuit should come on only when given the inputs 2, 3, 5 and 7. For all other inputs the light switch will be off.

## AND, OR and NOT Gate Functions

In our example, A and B are the inputs and F is the output. Figures 2 , 3, and 4 show AND, OR and NOT gate examples and their respective outputs. These gates will be used to design the combinational circuit in our problem definition. It is important to understand how these gates process inputs to get their corresponding outputs.

## The Truth Table

A truth table serves to show all the outputs for the combination of inputs to the system. Numerical inputs are converted to binary and the corresponding desired outputs are shown in Table 1.

## Our Basic Circuit

From Table 1 we can see that the binary translation of the inputs (2, 3, 5, 7) require 3 digits. This means that the number of switches which we require to give us all the combinations is 3. Our basic combinational circuit will therefore look like Figure 5.

## Simplifying our Boolean Expression

We now extract the min terms from the binary table and sum them in the following Boolean expression:

We now draw the actual combinational Logic circuit as seen in Figure 6.

## Designing our Combinational Circuit

To design our combinational circuit we perform the following steps:

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