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. Table 2.8 Boolean Expressionsfor the 16 Functions of TwoVariablesBooleanOperatorSymbolNameCommentsFunctionsBinary constantFO = 0NullF1 =xyx'yANDx and yF2 = x y'Inhibitionx, but not yF3=xTransferF4 =x'yylxInhibitiony, but not xF5= yTransferyF6 =x y'+x'y x® yExclusive- x or y, but notORbothF7=x+ yx+yORх огуF8 = (x+ y)' x yNORNot-ORF9 =x y +x'y'(x y )'Equivalence x equals yF 10 = y'y'Complement Not yF 11 = x + y'xCyImplication If y, then xF 12 = x'x'Complement Not xF 13 = x'+yx >yImplication If x, then yF 14 = (x y)'x t yNANDNot-ANDBinary constantF 15 = 1Identity

Writing the Ex-OR operation. A⊕B=AB'+A'B Writing the commutative and associative property.…

Answered: Table 2.8 Boolean Expressions for the…

Introductory Circuit Analysis (13th Edition)

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ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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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.

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.

$A \oplus B = A B' + A' B$

Writing the commutative and associative property.

$Commutative property : A \oplus B = B \oplus A Associative property : A \oplus (B \oplus C) = (A \oplus B) \oplus C$

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