电子教材-布尔代数和逻辑化简基础

Slide 1
New and Key Terms
• • • • •
Variable（变量） Complement（求补） Literal（字母） Sum term（和项） Product term（乘积项）
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 2
4-1 Boolean Operations and Expressions （布尔运算与表达式）
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
•The sum-of-product (SOP) form
Example: X = AB + CD + EF
•The product of sum (POS) form
Example: X = (A + B)(C + D)(E + F) Minimum SOP Expression
• The fewest possible product terms • The fewest possible literals per term
Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 21
Simplification Using Boolean Algebra
A simplified Boolean expression uses the fewest gates possible to implement a given expression. Method: to use the basic laws,rules and theorems of Boolean algebra.
Digital Fundamentals
CHAPTER 4 Boolean Algebra and Logic Simplification
（布尔代数和逻辑化简）
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 5
Laws of Boolean Algebra
• Commutative Laws（交换律） • Associative Laws（结合律） • Distributive Law（分配律）
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 3
Boolean Operations and Expressions
• Addition
0+0=0 0+1=1 1+0=1 1+1=1
• Multiplication
0*0=0 0*1=0 1*0=0 1*1 =1
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 22
EX 1： F = A BC + ABC + ABC
= ABC + AB(C + C) = ABC + AB = A(BC + B ) = A(C + B ) = AC + AB
提出AB =1
提出A 反变量吸收
Floyd Digital Fundamentals, 9/e
Slide 11
Rules of Boolean Algebra
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 10
Laws of Boolean Algebra
• Distributive Law: A(B + C) = AB + AC
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 16
DeMorgan’s Theorems
• Theorem 1
XY = X + Y
• Theorem 2
Remember: “Break the bar, change the sign”
X + Y = XY
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 7
Laws of Boolean Algebra
• Commutative Law of Multiplication:
A*B=B*A
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 8
Laws of Boolean Algebra
• Associative Law of Addition:
A + (B + C) = (A + B) + C
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 9
Laws of Boolean Algebra
• Associative Law of Multiplication:
A * (B * C) = (A * B) * C
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 20
New and Key Terms
Slide 6
Laws of Boolean Algebra
• Commutative Law of Addition:
A+B=B+A
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 12
Rules of Boolean Algebra
• Rule 10: A + AB = A
Proof:
Floyd Digital Fundamentals, 9/e
A+AB=A(1+B)=A•1=A
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 17
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 18
4-4 Boolean Analysis of Logic Circuits （逻辑电路的布尔分析）
Slide 4
4-2 Laws and Rules of Boolean Algebra （布尔代数的定理与规则）
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 19
4-5 Simplification Using Boolean Algebra （利用布尔代数进行逻辑化简）
Slide 15
4-3 DeMorgan’s Theorem （德·摩根定理）
Floyd Digital Fundamentals, 9/e
Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 14
Rules of Boolean Algebra
• Rule 12: (A + B)(A + C) = A + BC
Proof: ( A + B )( A + C) = AA + AB + AC + BC
= A(1 + B + C) + BC = A + BC
Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.
Slide 13
Rules of Boolean Algebra
wenku.baidu.com
• Rule 11: A + AB = A + B
Proof: A + AB = A + AB + AB
= A + B( A + A ) = A + B
Floyd Digital Fundamentals, 9/e Copyright ©2006 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.