Logic Design

المنطقي التصميمSecond Course

Syllabus Combinational Logic• The NAND Gate as a Universal Logic Element.• The NOR Gate as a Universal Logic Element.• Bit Parallel Adder.• Decoders.• Encoders.• Multiplexers.• De-multiplexersFlip-Flop• SR Flip-Flops.• D Flip-Flops.• JK Flip-Flops.Shift Register- Serial in \ Serial out shift Register Binary Counter- Asynchronous Binary Counter.- Synchronous Binary Counter.

Syllabus Combinational Logic• The NAND Gate as a Universal Logic Element.• The NOR Gate as a Universal Logic Element.• Bit Parallel Adder.• Decoders.• Encoders.• Multiplexers.• De-multiplexersFlip-Flop• SR Flip-Flops.• D Flip-Flops.• JK Flip-Flops.Shift Register- Serial in \ Serial out shift Register Binary Counter- Asynchronous Binary Counter.- Synchronous Binary Counter.

References1- Computer System Architecture Third

EditionM. Morris Mano

2 - Digital FundamentalsEight EditionFLOYD

3 - Digital FundamentalsNinth EditionFLOYD

4-Fundamentals of Digital Logic and Microcomputer DesignFifth edition

M.RAFIQZZAMAN

References1-Computer System Architecture Third

EditionM. Morris Mano

2 -Digital Fundamentals Eight EditionFLOYD

3 -Digital Fundamentals Ninth EditionFLOYD

4-Fundamentals of Digital Logic andMicrocomputer Design Fifth edition

M.RAFIQZZAMAN

•We have learned all the prerequisite material:

–Truth tables and Boolean expressions describe functions

–Expressions can be converted into hardware circuits

–Boolean algebra and K-maps help simplify expressions and

circuits

•Now, let us put all of these foundations to good use, to analyze

and design

some larger circuits

Introduction

• Logic circuits for digital systems may be

• A combinational circuit consists of logic gates whose outputs at any

time

are determined by the current input values, i.e., it has no memory

elements

• A sequential circuit consists of logic gates whose outputs at any

time

are determined by the current input values as well as the past input

values, i.e., it has memory elements.

• Each input and output variable is a binary variable

• 2^n possible binary input combinations

• One possible binary value at the output for each input combination

• A truth table or m Boolean functions can be used to specify input-output relation

A combinational circuit consists of :

1- Input variables.

2- Logic gates

3- Output variables

Logic gates accepts signals ( Binary signals) from inputs and generate signals to the

outputs.

an example that converts binary coded decimal (BCD) to the excess-

3 code for the decimal digits.

The bit combinations assigned to the BCD and excess-3 codes are

listed in Table. Since each code uses four bits to represent a decimal

digit, there mustbe four input variables and four output variables.

z = Dz = D

y = CD + CD = CD + 1C + D2y = CD + CD = CD + 1C + D2

x = BC + BD + BCD = B1C + D2 + BCDx = BC + BD + BCD = B1C + D2 + BCD

= B1C + D2 + B1C + D2= B1C + D2 + B1C + D2

w = A + BC + BD = A + B1C + D2w = A + BC + BD = A + B1C + D2

Half Adder

this circuit needs two binary inputs and two binary outputs. The input variables designate

the augend and addend bits; the output variables produce the sum and carry.

We assign symbols x and y to the two inputs and S (for sum) and C (for carry) to the

outputs. The truth table for the half adder is listed in Table. The C output is 1 only when

both inputs are 1. The simplified Boolean functions for the two outputs can be obtained

directly from the truth table. The simplified sum-of-products expressions are

S = xy + xy

C = xy

The logic diagram of the half adder implemented in sum of products is shown in Fig . It

can be also implemented with an exclusive-OR and an AND gate as shown in Fig . This

form is used to show that two half adders can be used to construct a full adder.

Full adderA full adder is a combinational circuit that forms the arithmetic sum of three bits. It

consists of three inputs and two outputs. Two of the input variables, denoted by x and y ,

represent the two significant bits to be added. The third input, z , represents the carry

from the previous lower significant position. Two outputs are necessary because the

arithmetic sum of three binary digits ranges in value from 0 to 3, and binary

representation of 2 or 3 needs two bits. The two outputs are designated by the symbols S

for sum and C for carry.

S = xyz + xyz + xyz + xyz C = xy + xz + yz