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Combinational Circuits

This document discusses combinational circuits and their analysis and design methods. It describes two types of logic circuits: combinational circuits whose outputs only depend on inputs, and sequential circuits whose outputs depend on both present inputs and state. It outlines the basic analysis procedure for combinational circuits and presents different design methods including gate-level and block-level approaches. Gate-level design is demonstrated through examples of a half adder, full adder, and code converters. Block-level design uses larger blocks or formulas and can build more complex circuits like a 4-bit parallel adder and BCD to excess-3 converter.

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63 views5 pages

Combinational Circuits

This document discusses combinational circuits and their analysis and design methods. It describes two types of logic circuits: combinational circuits whose outputs only depend on inputs, and sequential circuits whose outputs depend on both present inputs and state. It outlines the basic analysis procedure for combinational circuits and presents different design methods including gate-level and block-level approaches. Gate-level design is demonstrated through examples of a half adder, full adder, and code converters. Block-level design uses larger blocks or formulas and can build more complex circuits like a 4-bit parallel adder and BCD to excess-3 converter.

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Combinational Circuits

Two Classes of Logic Circuits

 Combinational Circuit
o Each outputs depends entirely on the immediate input.
 Sequential Circuit
o Each output depends on both present inputs and state.

Analysis Procedure

 Steps
1. Label the Inputs and Outputs
2. Obtain the functions of intermediate points and the outputs.
3. Draw the truth table.
4. Deduce the functionality of the circuit.

Design Methods

Different Combinational Circuit Design Methods

 Gate-Level Design Method (With Logic Gates)


 Block-Level Design Method (With Functional Blocks)

Gate-Level Design: Half Adder

 Design Procedure
o State Problem
o Determine and label the inputs and outputs of circuit.
o Draw the truth table.
o Obtain simplified Boolean functions.
o Draw the Logic Diagram

Gate-Level Design: Full Adder

 Half adder adds up only two bits


 To add two binary numbers, we need to add 3 bits (including the carry)

Gate-Level (SSI) Design: Code Converters

 Takes an input code, translates to its equivalent output code.


 Example, BCD to Excess-3 Code Converter
Block-Level Design

 More complex circuits can also be built using block-level method


 In general, block-level design method (as opposed to gate-level design) relies on algorithms
or formulae of the circuit, which are obtained by decomposing the main problem to sub-
problems recursively (until small enough to be directly solved by blocks of circuits)
 First example shows how to create a 4-bit parallel adder using block-level design
 Using 4-bit parallel adders as building blocks, we can create
o BCD-to-Excess-3 Code Converter
o 16-bit Parallel Adder

4 Bit Parallel Adder

 Adds two 4-bit numbers together and a carry-in to produce a 5 bit result

 Use an alternative design.


o Addition formula for each pair of bits (with carry in)

BCD to Excess 3 Converter using Block Level Design

 Excess-3 Code can be converted from BCD code using truth tables.
 Gate-Level Design can be used since only 4 inputs.
 Use problem-specific formula.
o Excess-3 Code = BCD Code + 0011

16 Bit Parallel Adder

 Larger parallel adders can be built from smaller ones.


 A 16-bit parallel adder can be constructed from four 4-bit parallel adders.
Magnitude Comparator

 A device that compares 2 unsigned values A and B, to check if A > B, A =B, or A<B

Circuit Delays

 Given a logic gate with delay t. If inputs are stable at times t1,t2,…., then the earliest time in
which the output will be stable is : max (t1,t2,…) + t
 To calculate the delays of all outputs of a combinational circuit, repeat above rule for all
gates.

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