Combinational Circuit - Analysis

Tags: #◇Computer Science #◇CSARCH1 #◇Problem Solving #◇M4

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◇Overview

This sub-module discusses the analysis procedure for combinational circuits.
Objective: Learn how to analyze combinational circuits.

◇Concepts & Definitions

Combinational Circuits

A combinational logic circuit has:

• A set of $m$ Boolean inputs.
• A set of $n$ Boolean outputs.
• $n$ switching functions, each mapping the $2^m$ input combinations to an output such that the current output depends only on the current input values (no memory or feedback).

◇Analysis Procedure

The objective of analysis is to obtain output Boolean functions or truth tables from logic diagrams.

Deriving Boolean Functions

1. Label Inputs/Outputs: Label all gate outputs that are a function of input variables. Determine the Boolean functions for each gate output.
2. Intermediate Labels: Label the gates that are a function of input variables and previously labeled gates. Find the Boolean functions for these gates.
3. Iterate: Repeat step 2 until the outputs of the circuit are obtained.
4. Substitution: By repeated substitution of previously defined intermediate functions, obtain output Boolean functions in terms of input variables alone.

Deriving the Truth Table

1. Determine Input Combinations: For $n$ inputs, form $2^n$ possible input combinations (i.e., binary numbers from 0 to $2^n - 1$).
2. Label Gates: Label the outputs of selected gates.
3. Evaluate Simple Gates: Obtain truth table columns for outputs of gates which are functions of the input variables only.
4. Evaluate Downstream Gates: Proceed to obtain truth table columns for outputs of gates which are functions of previously defined values until columns for all outputs are determined.

◇References & Navigation

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