Digital Logic Circuit Notes | BTech. CS

Digital Logic Circuit Notes

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The following Digital Logic Circuit Notes on the subject of Computer Organisation and Architecture will surely help you to achieve grace marks.

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Digital Computer

  • A binary digit is called a bit.
  • Information is represented in digital computers in groups of bits.
  • A computer system is subdivided into Hardware and Software
  • The computer’s hardware consists of all the electronic components and electromechanical devices that comprise the physical entity of the device.
  • Computer software consists of the instructions and data that the computer manipulates to perform various data-processing tasks.
  • A sequence of instructions for the computer is called a program.
  • The programs included in a systems software package are referred to as the operating system.
  • The hardware of the computer is usually divided into three major parts :
    • Central Processing Unit (CPU)
    • Random Access Memory (RAM)
    • Input-Output Processor (IOP)
Digital Logic Circuit Notes

Difference between Computer Organisation and Computer Architecture

Computer OrganisationComputer Architecture
Concerned with the hardware design of the computerConcerned with the functional behavior of the computer
Describes how things are doneDescribes what has to be done
Deals with low-level designsDeals with high-level designs
The implementation of the architecture is called the organizationAs a programmer, you can view architecture as a series of instructions, addressing modes, and registers
Consists of physical units like circuit designs, peripherals, and addersComprises logical functions such as instruction sets, registers, data types, and addressing modes

Logic Gates

  • Binary information is represented in digital computers by physical quantities called signals.
  • The two states represent a binary variable that can be equal to 1 or 0.
  • For example, a particular digital computer may employ a signal of 3 volts to represent binary 1 and 0.5 volts to represent binary 0.
  • The manipulation of binary information is done by logic circuits called gates.
  • Each gate has a distinct graphic symbol and its operation can be described by means of an algebraic expression.
  • The input-output relationship of the binary variables for each gate can be represented in tabular form by a truth table.

Also Read: Digital Component Notes

AND Gate

Digital Logic Circuit Notes, AND Gate
Logic Diagram of AND Gate

Algebraic function – x = A x B

Digital Logic Circuit Notes, AND Truth Table
Truth Table of AND Gate

OR Gate

Digital Logic Circuit Notes, OR Gate
Logic Diagram of OR Gate

Algebraic function – x = A + B

Digital Logic Circuit Notes, OR Truth Table
Truth Table of OR Gate

NAND Gate

Digital Logic Circuit Notes, NAND Gate
Logic Diagram of NAND Gate

Algebraic function – x = (A x B)’

Digital Logic Circuit Notes, NAND Truth Table
Truth Table of NAND Gate

NOR Gate

Digital Logic Circuit Notes, NOR Gate
Logic Diagram of NOR Gate

Algebraic function – x = (A + B)’

Digital Logic Circuit Notes, NOR Truth Table
Truth Table of NOR Gate

Buffer Gate

Digital Logic Circuit Notes, Buffer Gate
Logic Diagram of Buffer Gate

Algebraic function – x = A

Digital Logic Circuit Notes, Buffer Truth Table
Truth Table of Buffer Gate

NOT Gate

Digital Logic Circuit Notes, NOT Gate
Logic Diagram of NOT Gate

Algebraic function – x = A’

Digital Logic Circuit Notes, NOT Truth Table
Truth Table of NOT Gate

XOR Gate

Digital Logic Circuit Notes, XOR Gate
Logic Diagram of XOR Gate

Algebraic function – x = A ⊕ B or A’B + B’A

Digital Logic Circuit Notes, XOR Truth Table
Truth Table of XOR Gate

XNOR Gate

Digital Logic Circuit Notes, XNOR Gate
Logic Diagram of XNOR Gate

Algebraic function – x = (A ⊕ B)’ or A’B’ + AB

Digital Logic Circuit Notes, XNOR Truth Table
Truth Table of XNOR Gate

Boolean Algebra

  • Boolean algebra is an algebra that deals with binary variables and logic operations.
  • For a given value of the variables, the Boolean function can be either 1 or 0.
  • Ex – F = x + y’z

Basic identities: –

x + 0 = xx.0 = 0
x + 1 = xx.1 = x
x + x =xx.x = x
x + x’ =1x.x’ = 0
x + y = y + xx.y = y.x
x + ( y + z ) = ( x + y ) + zx ( y.z ) = ( x.y ) z
x ( y + z ) = x.y + x.zx + y.z = ( x + y ).( x + z )
( x + y ) ‘ = x’.y ‘( x.y )’ = x’ + y’
( x’ ) ‘ = xx + x.y = x

De-Morgan’s Law:-

  • ( x.y )’ = x’ + y’
  • ( x + y )’ = x’.y’

Canonical and Standard Form

  • Canonical Form – Boolean function can be expressed as Canonical Disjunctive Normal Form known as minterm and some are expressed as Canonical Conjunctive Normal Form known as maxterm
  • In Minterm, we look for the functions where the output results in “1”
  • Maxterm we look for a function where the output results in “0”. 
  • We perform the Sum of minterm also known as the Sum of products (SOP). 
    We perform Product of Maxterm also known as Product of sum (POS).
xyzMinterms (SOP)Maxterms (POS)
000m0 = x’.y’.z’ = min(x’,y’,z’)M0 = x + y +z = max(x,y,z)
001m1 = x’.y’.z = min(x’,y’,z)M1 = x + y +z’ = max(x,y,z’)
010m2 = x’.y.z’ = min(x’.y.z’)M2 = x + y’ + z = max(x,y’,z)
011m3 = x’.y.z = min(x’.y.z)M3 = x + y’ + z’ = max(x,y’,z’)
100m4 = x.y’.z’ = min(x,y’,z’)M4 = x’ + y + z = max(x’,y,z)
101m5 = x.y’.z = min(x,y’,z)M5 = x’ + y + z’ = max(x’,y,z’)
110m6 = x.y.z’ = min(x,y,z’)M6 = x ‘+ y’ + z = max(x’,y’,z)
111m7 = x.y.z = min(x,y,z)M7 = x’ + y’ + z’ = max(x’,y’,z’)

Combinational Circuit

  • A combinational circuit is a connected arrangement of logic gates with a set of inputs and outputs.
  • The n binary input variables come from an external source, the m binary output variables go to an external destination, and in between there is an interconnection of logic gates.

Half Adder

  • A combinational circuit that performs the addition of two bits
  • The input variables of a half-adder are called the augend and added bits
  • The output variables are the sum (S) and carry (C)
  • The sum represents the least significant bit
  • Example – 1 + 1 = 10. Here S = 0 and C = 1
  • S = x’.y + x.y’ = x ⊕ y
  • c = x.y
Digital Logic Circuit Notes, Half Adder Truth Table
Truth Table of Half Adder
Digital Logic Circuit Notes, Half Adder Logic Design
Logic Diagram of Half Adder
Digital Logic Circuit Notes, Half Adder Block Diagram
Block Diagram of Half Adder

Full Adder

  • A combinational circuit that forms the arithmetic sum of three input 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 previous lower significant position carry.
  • Two half-adders are needed to implement a full adder.
Digital Logic Circuit Notes, Full Adder Truth Table
Truth Table of Full Adder
Digital Logic Circuit Notes, Full Adder Logic Diagram
Logic Diagram of Full Adder
Digital Logic Circuit Notes, Full Adder Block Diagram
Block Diagram of Full Adder

Final Words

From the above article, you must have gained knowledge about Digital Logic circuits. We hope that with the help of these notes you will be successful.

Also Read: Digital Component Notes

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