Basics of Digital ElectronicsCourse: B.Sc.(CS)Sem.:1st

LOGIC CIRCUITS:

1) Combinational

2) Sequential

Combinational logic circuits (circuits without a memory):

Combinational switching networks whose outputs depend only on the current inputs.

Sequential logic circuits (circuits with memory):

In this kind of network, the outputs depend on the current inputs and the previous inputs. These networks employ storage elements and logic gates.

COMBINATIONAL CIRCUITS

Most important standard combinational circuits are:• Adders• Subtractors• Comparators• Decoders• Encoders• Multiplexers

Available in IC’s as MSI and used asstandard cells in complex VLSI (ASIC)

ANALYSIS OF COMBINATIONAL LOGIC

ANALYSIS OF COMBINATIONAL LOGIC

ANALYSIS OF COMBINATIONAL LOGIC

DESIGN OF COMBINATIONAL LOGIC1. From the specifications of the circuit, determine the

number of inputs and outputs

2. Derive the truth table that defines the relationship between the input and the output.

3. Obtain the simplified Boolean function using x-variable K-Map.

4. Draw the logic diagram and verify the correctness of the design.

DESIGN OF COMBINATIONAL LOGIC Example: Design a combinational circuit with three

inputs and one output. The output is a 1 when the binary value is less than three.

The output is 0 otherwise.

BINARY ADDER – Half Adder

Implementation of Half Adder

BINARY ADDER - Full Adder

Full Adder in SOP

Implementation Full Adder with two half Adders

4-BIT FULL ADDER

4 bit Adder

Magnitude Comparator A magnitude comparator is a combinational circuit that

compares two numbers, A and B, and then determines their relative magnitudes.

A > B A = B A < B Algorithm Consider two numbers, A and B, with four digits

each: A=A3 A2 A1 A0

B=B3 B2 B1 B0

xi=1 if A=B=0 or A=B=1 xi=AiBi+ Ai’Bi’ for i=0,1,2,3 XNOR For equality to exist, all xi variables must be equal to 1: (A=B)=X3 X2 X1 X0

AND Operation

Magnitude Comparator To determine if A is greater than or less than B, we

inspect the relative magnitudes of significant digits.

If the two digits are equal, we compare the next lower significant pair of digits. The comparison continues until a pair of unequal digits is reached.

The sequential comparison can be expressed by:

DECODERS

A decoder is a combinational circuit that converts binary information

from n input lines to an 2nunique output lines.

Some Applications:

a) Microprocessor memory system: selecting different banks of memory.

b) Microprocessor I/O: Selecting different devices.

c) Memory: Decoding memory addresses (e.g. in ROM).

d) Decoding the binary input to activate the LED segments so that the decimal number can be displayed.

3-to-8-line DECODER

If the input corresponds to minterm mi then the decoder ouput i will be the single asserted output.

3-to-8-line DECODER

2-to-4-line DECODER with Enable The decoder is enabled when E = 0. The output whose

value = 0 represents the minterm is selected by inputs A and B.

The decoder is inactive when E=1 D0………D3 =1

A Decoder with enable input is called a decoder/demultiplexer. Demultiplexer receives information from a single line and directs it to the output lines.

A 4 x 16 DECODER When w = 0, the top decoder is enabled and the bottom is

disabled. Top decoder generates 8 minterms 0000 to 0111, while the

bottom decoder outputs are 0’s. When w = 1, the top decoder is disabled and the bottom is

enabled. Bottom decoder generates 8 minterms 1000 to 1111, while

the top decoder outputs are 0’s.

Full-Adder using Decoder

MULTIPLEXERS/DATA SELECTORS A multiplexer is a combinational circuit that selects

one of many input lines (2n ) and steers it to its single output line. There are (2n ) and n selection lines whose bit combinations determine which input is selected.

4-to-1LINE MULTIPLEXER DESIGN

In general, a 2n –to–1- line multiplexer is constructed from an n–to 2n decoder by adding to 2n it lines, one to each AND gate.

References Digital Logic and Computer Design – M. Morris Mano

– Pearson

Fundamentals of Digital Circuits – A. Anand Kumar -PHI

Digital Electronics - Gothmen - PHI

Digital Electronics Principles - Malvino & Leech -MGH

Digital Electronics -Tokneinh - MGH

Web References www.engrcs.com/courses/engr250/engr250lecture.pdf

www.eng.auburn.edu/~strouce/class/elec4200/design

en.wikipedia.org/wiki/Combinational_logic

www.allaboutcircuits.com › ... › Combinational Logic Functions

www.cs.umd.edu/class/sum2003/cmsc311/Notes/Comb/gates.htm