Download presentation

Presentation is loading. Please wait.

Published byRobert Kilner Modified over 2 years ago

1
Combinational Logic Circuits Chapter 2 Mano and Kime

2
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

3
Digital Logic Gates *

4
Gates with More than Two Inputs

5
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

6
Basic Identities of Boolean Algebra

7
Implementation of Boolean Function with Gates

8
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

9
Minterms for Three Variables

10
Sum of Products Design X Y minterms 0 0 m0 = !X & !Y 0 1 m1 = !X & Y 1 0 m2 = X & !Y 1 1 m3 = X & Y

11
Sum of Products Design X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate m1 = !X & Y m2 = X & !Y Z = m1 + m2 = (!X & Y) + (X & !Y)

12
Sum of Products: Exclusive-OR !X & Y X & !Y Z = (!X & Y) + (X & !Y)

13
Maxterms for Three Variables

14
Product of Sums Design Maxterms: A maxterm is NOT a minterm maxterm M0 = NOT minterm m0 M0 = m0’ =(X’. Y’)’ = (X + Y)” = X + Y

15
Product of Sums Design X Y minterms maxterms 0 0 m0 = !X. !Y M0 = !m0 = X + Y 0 1 m1 = !X. Y M1 = !m1 = X + !Y 1 0 m2 = X. !Y M2 = !m2 = !X + Y 1 1 m3 = X. Y M3 = !m3 = !X + !Y

16
Product of Sums Design X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate Z is NOT minterm m0 AND it is NOT minterm m3

17
Product of Sums Design X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 Design an XOR gate M0 = X + Y M3 = !X + !Y Z = M0 & M3 = (X + Y) & (!X + !Y)

18
Product of Sums: Exclusive-OR

19
Three- Level and Two- Level Implementation

20
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

21
Two-Variable Map

22
Three-Variable Map

23
Three- Variable Map: Flat and on a Cylinder to Show Adjacent Squares

24
Three-variable K-Maps X YZ 00011110 0 1 11 11 F = !X & !Y + X & Z

25
Three-variable K-Maps X YZ 00011110 0 1 11 11 F = !X & !Y & !Z + !X & !Y & Z + X & !Y & Z + X & Y & Z F = !X & !Y & (!Z + Z) + X & Z & (!Y + Y) = !X & !Y + X & Z

26
Three-variable K-Maps X YZ 00011110 0 1 1 1 11 F = Y & !Z + X 1

27
Three-variable K-Maps X YZ 00011110 0 1 11 111 1 F = !X & !Y + X & y + Z

28
Three-variable K-Maps X YZ 00011110 0 1 11 11 F = X & Z + !X & !Z

29
Three-variable K-Maps X YZ 00011110 0 1 11 11 1 1 F = Y + !Z

30
Three-variable K-Maps X YZ 00011110 0 1 0123 4567 11 11 F = m0 + m2 + m5 + m7 = (0,2,5,7)

31
Four-Variable Map

32
Four-Variable Map: Flat and on a Torus to Show Adjacencies

33
Four-variable K-Maps WX YZ 00011110 00 01 11 10 0 1 3 2 4 5 7 6 8 9 13 15 14 11 10 12 Each square is numbered in the above K-map

34
Four-variable K-Maps WX YZ 00011110 00 01 11 10 0123 4567 89 11 12131415 F(W,X,Y,Z) = (2,4,5,6,7,9,13,14,15)

35
Four-variable K-Maps 111 1 1 WX YZ 00011110 00 01 11 10 111 1 F = !W & X + X & Y + !W & Y & !Z + W & !Y & Z

36
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

37
Prime Implicants F = XY’Z + X’Z’ + X’Y Each product term is an implicant A product term that cannot have any of its variables removed and still imply the logic function is called a prime implicant.

38
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

39
Digital Logic Gates >

40
>

41
Logical Operations with NAND Gates

42
Alternative Graphics Symbols for NAND and NOT Gates

43
Logical Operations with NOR Gates

44
Two Graphic Symbols for NOR Gate

45
Generalized De Morgan’s Theorem NOT all variables Change & to + and + to & NOT the result -------------------------------------------- F = X & Y + X & Z + Y & Z F = !((!X + !Y) & (!X + !Z) & (!Y + !Z)) F = !(!(X & Y) & !(X & Z) & !(Y & Z))

47
NAND Gate

48
X Y X Z Y Z F F = X & Y + X & Z + Y & Z

49
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

50
Exclusive-OR Gate XOR X Y Z Z = X $ Y X Y Z 0 0 0 0 1 1 1 0 1 1 1 0 X $ 0 = X X $ 1 = !X X $ X = 0 X $ !X = 1 X $ !Y = !(X $ Y) !X $ Y = !(X $ Y) A $ B = B $ A (A $ B) $ C = A $ (B $ C) = A $ B $ C

51
Exclusive-OR Constructed with NAND gates X & (!X + !Y) + Y & (!X + !Y) = X & !X + X & !Y + Y & !X + Y & !Y = X & !Y + Y & !X = X & !Y + !X & Y = X $ Y

52
Parity Generation and Checking

53
Combinational Logic Circuits Binary Logic and Gates Boolean Algebra Standard Forms Map Simplification NAND and NOR Gates Exclusive-OR Gates Integrated Circuits

54
Fully Complementary CMOS Gate Structure and Examples An Integrated circuit (IC) is a silicon semiconductor crystal, containing the components for the digital gates. The various gates are connected on the chip to form the IC.

Similar presentations

Presentation is loading. Please wait....

OK

CS 121 Digital Logic Design

CS 121 Digital Logic Design

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on trade fair 2016 Ppt on acid-base titration indicator Ppt on 2 dimensional figures and 3 dimensional slides to digital Ppt online open enrollment Thyroid anatomy and physiology ppt on cells Ppt on adobe photoshop tools Ppt on triangles for class 9th free download Ppt on life cycle of silk moth Ppt on team building training module Ppt on magnetic lines of force