Download presentation

Presentation is loading. Please wait.

Published byGriffin Munt Modified over 3 years ago

1
CENG 241 Digital Design 1 Lecture 3 Amirali Baniasadi amirali@ece.uvic.ca

2
2 This Lecture zReview of last lecture zBoolean Algebra

3
3 Canonical & Standard Forms zConsider two binary variables x, y and the AND operation zfour combinations are possible: x.y, x’.y, x.y’, x’.y’ zeach AND term is called a minterm or standard products zfor n variables we have 2 n minterms zConsider two binary variables x, y and the OR operation zfour combinations are possible: x+y, x’+y, x+y’, x’+y’ zeach OR term is called a maxterm or standard sums zfor n variables we have 2 n maxterms

4
4 Minterms zx y z Terms Designation z 0 0 0 x’.y’.z’ m0 z 0 0 1 x’.y’.z m1 z 0 1 0 x’.y.z’ m2 z 0 1 1 x’.y.z m3 z 1 0 0 x.y’.z’ m4 z 1 0 1 x.y’.z m5 z 1 1 0 x.y.z’ m6 z 1 1 1 x.y.z m7

5
5 Maxterms zx y z Designation Terms z 0 0 0 M0 x+y+z z 0 0 1 M1 x+y+z’ z 0 1 0 M2 x+y’+z z 0 1 1 M3 x+y’+z’ z 1 0 0 M4 x’+y+z z 1 0 1 M5 x’+y+z’ z 1 1 0 M6 x’+y’+z z 1 1 1 M7 x’+y’+z’

6
6 Boolean Function: Exampl How to express algebraically z1.Form a minterm for each combination forming a 1 z2.OR all of those terms zTruth table example: zx y z F1 minterm z 0 0 0 0 z 0 0 1 1 x’.y’.z m1 z 0 1 0 0 z 0 1 1 0 z 1 0 0 1 x.y’.z’ m4 z 1 0 1 0 z 1 1 0 0 z 1 1 1 1 x.y.z m7 zF1=m1+m4+m7=x’.y’.z+x.y’.z’+x.y.z=Σ(1,4,7)

7
7 Boolean Function: Exampl How to express algebraically z1.Form a maxterm for each combination forming a 0 z2.AND all of those terms zTruth table example: zx y z F1 maxterm z 0 0 0 0 x+y+z M0 z 0 0 1 1 z 0 1 0 0 x+y’+z M2 z 0 1 1 0 x+y’+z’ M3 z 1 0 0 1 z 1 0 1 0 x’+y+z’ M5 z 1 1 0 0 x’+y’+z M6 z 1 1 1 1 zF1=M0.M2.M3.M5.M6 = л(0,2,3,5,6)

8
8 Implementations Three-level implementation vs. two-level implementation Two-level implementation normally preferred due to delay importance.

9
9 Digital Logic Gates

10
10 Integrated Circuits (ICs) zLevels of Integration zSSI: fewer than 10 gates on chip zMSI:10 to 1000 gates on chip zLSI: thousands of gates on chip zVLSI:Millions of gates on chip z Digital Logic Families zTTL transistor-transistor logic zECL emitter-coupled logic zMOS metal-oxide semiconductor zCMOS complementary metal-oxide semiconductor

11
11 Digital Logic Parameters zFan-out: maximum number of output signals zFan-in : number of inputs zPower dissipation zPropagation delay zNoise margin: maximum noise

12
12 Gate-Level Minimization zThe Map Method: zA simple method for minimizing Boolean functions zMap: diagram made up of squares zEach square represents a minterm

13
13 Two-Variable Map

14
14 Two-Variable Map Maps representing x.y and x+y

15
15 Three-Variable Map

16
16 Three-Variable Map Minterms are not arranged in a binary sequence Minterms arranged in gray code: Only one bit changes from one column to the next

17
17 Three-Variable Map Each variable is 1 in 4 squares, 0 in 4 squares Variable appears unprimed in squares equal to 1 Variable appears primed in squares equal to 0 Each variable is 1 in 4 squares, 0 in 4 squares

18
18 Three-Variable Map-example 1 Sum of two adjacent minterms can be simplified to a single AND term consisting of two literals

19
19 Three-Variable Map-example 2

20
20 Three-Variable Map-example 3

21
21 Three-Variable Map-example 4

22
22 Four-Variable Map

23
23 Four-Variable Map-example 1 1

24
24 Four-Variable Map-example 2

25
25 HW #1 zHW #1- Due Friday, May 23rd (4:00 PM) zSolve the following problems from the textbook (5th edition): 2-20, 2-21. 3-2, 3-4, 3-5 and 3-12.

26
26 Summary zExtension to multiple inputs zPositive & Negative Logic zIntegrated Circuits zGate Level Minimization

Similar presentations

OK

CS105 Introduction to Computer Concepts GATES and CIRCUITS

CS105 Introduction to Computer Concepts GATES and CIRCUITS

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on our changing earth Ppt on c language overview Ppt on electricity for class 10th exercise Ppt on accounting standards 10 Ppt on satellite orbit chart Ppt on secret of success Ppt on spirituality in daily life Ppt on surface water pump Ppt on historical monuments of india Ppt on great indian mathematicians