CHAPTER III BOOLEAN ALGEBRA

INTRO. TO COMP. ENG. CHAPTER III-1

BOOLEAN ALGEBRA

?CHAPTER III

CHAPTER III BOOLEAN ALGEBRA

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INTRO. TO COMP. ENG. CHAPTER III-2

BOOLEAN ALGEBRA

BOOLEAN VALUES

INTRODUCTION

?BOOLEAN VALUES

? Boolean algebra is a form of algebra that deals with single digit binary values and variables.

? Values and variables can indicate some of the following binary pairs of values: ? ON / OFF ? TRUE / FALSE ? HIGH / LOW ? CLOSED / OPEN ? 1/0

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INTRO. TO COMP. ENG. CHAPTER III-3

BOOLEAN ALGEBRA

BOOL. OPERATIONS

?BOOLEAN VALUES -INTRODUCTION

FUNDAMENTAL OPERATORS

? Three fundamental operators in Boolean algebra

? NOT: unary operator that complements represented as A , A , or A

? AND: binary operator which performs logical multiplication

? i.e. A ANDed with B would be represented as AB or A B

? OR: binary operator which performs logical addition

? i.e. A ORed with B would be represented as A + B

NOT

AND

OR

AA

01 10

A B AB 00 0 01 0

A B A+B 00 0 01 1

10 0

10 1

11 1

11 1

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BOOL. OPERATIONS INTRO. TO COMP. ENG. CHAPTER III-4

?BOOLEAN OPERATIONS -FUNDAMENTAL OPER.

BOOLEAN ALGEBRA BINARY BOOLEAN OPERATORS

? Below is a table showing all possible Boolean functions FN given the twoinputs A and B .

A B F0 F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 000000000011111111 010000111100001111 100011001100110011 110101010101010101

0 AB A

B A+B

B

A AB 1

Null

AB

AB

Identity

Inhibition

A+B

Implication

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INTRO. TO COMP. ENG. CHAPTER III-5

BOOLEAN ALGEBRA

BOOLEAN ALGEBRA ?BOOLEAN OPERATIONS -FUNDAMENTAL OPER.

PRECEDENCE OF OPERATORS -BINARY BOOLEAN OPER.

? Boolean expressions must be evaluated with the following order of operator

precedence

? parentheses ? NOT ? AND ? OR

Example: F = (A(C + BD) + BC)E

F = A C+ BD + BC E

{{{

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