Table 2.8 Boolean Expressions for the 16 Functions of Two Variables Boolean Operator Symbol Name Comments Functions Binary constant FO = 0 Null F1 =xy x'y AND x and y F2 = x y' Inhibition x, but not y F3=x Transfer F4 =x'y ylx Inhibition y, but not x F5= y Transfer y F6 =x y'+x'y x® y Exclusive- x or y, but not OR both F7=x+ y x+y OR х огу F8 = (x+ y)' x y NOR Not-OR F9 =x y +x'y'(x y )' Equivalence x equals y F 10 = y' y' Complement Not y F 11 = x + y' xCy Implication If y, then x F 12 = x' x' Complement Not x F 13 = x'+y x >y Implication If x, then y F 14 = (x y)' x t y NAND Not-AND Binary constant F 15 = 1 Identity
Table 2.8 Boolean Expressions for the 16 Functions of Two Variables Boolean Operator Symbol Name Comments Functions Binary constant FO = 0 Null F1 =xy x'y AND x and y F2 = x y' Inhibition x, but not y F3=x Transfer F4 =x'y ylx Inhibition y, but not x F5= y Transfer y F6 =x y'+x'y x® y Exclusive- x or y, but not OR both F7=x+ y x+y OR х огу F8 = (x+ y)' x y NOR Not-OR F9 =x y +x'y'(x y )' Equivalence x equals y F 10 = y' y' Complement Not y F 11 = x + y' xCy Implication If y, then x F 12 = x' x' Complement Not x F 13 = x'+y x >y Implication If x, then y F 14 = (x y)' x t y NAND Not-AND Binary constant F 15 = 1 Identity
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
By substituting the Boolean expression equivalent of the binary operations as defined in Table 2.8 , show the following: The exclusive-OR operation is commutative and associative.
Transcribed Image Text:Table 2.8 Boolean Expressions
for the 16 Functions of Two
Variables
Boolean
Operator
Symbol
Name
Comments
Functions
Binary constant
FO = 0
Null
F1 =xy
x'y
AND
x and y
F2 = x y'
Inhibition
x, but not y
F3=x
Transfer
F4 =x'y
ylx
Inhibition
y, but not x
F5= y
Transfer
y
F6 =x y'+x'y x® y
Exclusive- x or y, but not
OR
both
F7=x+ y
x+y
OR
х огу
F8 = (x+ y)' x y
NOR
Not-OR
F9 =x y +x'y'(x y )'
Equivalence x equals y
F 10 = y'
y'
Complement Not y
F 11 = x + y'
xCy
Implication If y, then x
F 12 = x'
x'
Complement Not x
F 13 = x'+y
x >y
Implication If x, then y
F 14 = (x y)'
x t y
NAND
Not-AND
Binary constant
F 15 = 1
Identity
Expert Solution
Step 1
Writing the Ex-OR operation.
Writing the commutative and associative property.
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