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3.8 EXCLUSIVE-OR FUNCTION The exclusive-OR (XOR), denoted by the symbol ®, is a logical operation that performs the following Boolean operation: x®y=xy'+x'y The exclusive-OR is equal to 1 if only x is equal to 1 or if only y is equal to 1 (i.e., x and y differ in value), but not when both are equal to 1 or when both are equal to 0. The exclusive-NOR, also known as equivalence, performs the following Boolean operation: (x®y}=xy+x°y' The exclusive-NOR is equal to 1 if both x and y are equal to 1 or if both are equal to 0. The exclusive-NOR can be shown to be the complement of the exclusive-OR by means of a truth table or by algebraic manipulation: (x®y)=(xy'+x'y)'=(x'+y)(x+y')=xy+x'y' The following identities apply to the exclusive-OR operation: x®0=x x®1=x' x®x=0 x®x'=1 x®y'=x'®y=(x®y)' Any of these identities can be proven with a truth table or by replacing the e operation by its equivalent Boolean expression. Also, it can be shown that the exclusive-OR operation is both commutative and associative; that is, A®B=B®A and (A®B)®C=A®(B®C)=A®B®C This means that the two inputs to an exclusive-OR gate can be interchanged without affecting the operation. It also means that we can evaluate a three-variable exclusive-OR operation in any order, and for this reason, three or more variables can be expressed without parentheses. This

3.8 EXCLUSIVE-OR FUNCTION The exclusive-OR (XOR), denoted by the symbol ®, is a logical operation that performs the following Boolean operation: x®y=xy'+x'y The exclusive-OR is equal to 1 if only x is equal to 1 or if only y is equal to 1 (i.e., x and y differ in value), but not when both are equal to 1 or when both are equal to 0. The exclusive-NOR, also known as equivalence, performs the following Boolean operation: (x®y}=xy+x°y' The exclusive-NOR is equal to 1 if both x and y are equal to 1 or if both are equal to 0. The exclusive-NOR can be shown to be the complement of the exclusive-OR by means of a truth table or by algebraic manipulation: (x®y)=(xy'+x'y)'=(x'+y)(x+y')=xy+x'y' The following identities apply to the exclusive-OR operation: x®0=x x®1=x' x®x=0 x®x'=1 x®y'=x'®y=(x®y)' Any of these identities can be proven with a truth table or by replacing the e operation by its equivalent Boolean expression. Also, it can be shown that the exclusive-OR operation is both commutative and associative; that is, A®B=B®A and (A®B)®C=A®(B®C)=A®B®C This means that the two inputs to an exclusive-OR gate can be interchanged without affecting the operation. It also means that we can evaluate a three-variable exclusive-OR operation in any order, and for this reason, three or more variables can be expressed without parentheses. This

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Show that the output carry in a full-adder circuit can be expressed in the AND–OR–INVERT form C i + 1 = G i + P i C i = ( G i ′ P i ′ + G i ′ C i ′ ) ′ (IC type 74182 is a lookahead carry generator circuit that generates the carries with AND–OR–INVERT gates (see Section 3.8 ). The circuit assumes that the input terminals have the complements of the G’s, the P’s, and of C 1 . Derive the Boolean functions for the lookahead carries C 2 , C 3 , and C 4 in this IC.

3.8 EXCLUSIVE-OR FUNCTION The exclusive-OR (XOR), denoted by the symbol ®, is a logical operation that performs the following Boolean operation: x®y=xy'+x'y The exclusive-OR is equal to 1 if only x is equal to 1 or if only y is equal to 1 (i.e., x and y differ in value), but not when both are equal to 1 or when both are equal to 0. The exclusive-NOR, also known as equivalence, performs the following Boolean operation: (x®y}=xy+x°y' The exclusive-NOR is equal to 1 if both x and y are equal to 1 or if both are equal to 0. The exclusive-NOR can be shown to be the complement of the exclusive-OR by means of a truth table or by algebraic manipulation: (x®y)=(xy'+x'y)'=(x'+y)(x+y')=xy+x'y' The following identities apply to the exclusive-OR operation: x®0=x x®1=x' x®x=0 x®x'=1 x®y'=x'®y=(x®y)' Any of these identities can be proven with a truth table or by replacing the e operation by its equivalent Boolean expression. Also, it can be shown that the exclusive-OR operation is both commutative and associative; that is, A®B=B®A and (A®B)®C=A®(B®C)=A®B®C This means that the two inputs to an exclusive-OR gate can be interchanged without affecting the operation. It also means that we can evaluate a three-variable exclusive-OR operation in any order, and for this reason, three or more variables can be expressed without parentheses. This
Transcribed Image Text:3.8 EXCLUSIVE-OR FUNCTION The exclusive-OR (XOR), denoted by the symbol ®, is a logical operation that performs the following Boolean operation: x®y=xy'+x'y The exclusive-OR is equal to 1 if only x is equal to 1 or if only y is equal to 1 (i.e., x and y differ in value), but not when both are equal to 1 or when both are equal to 0. The exclusive-NOR, also known as equivalence, performs the following Boolean operation: (x®y}=xy+x°y' The exclusive-NOR is equal to 1 if both x and y are equal to 1 or if both are equal to 0. The exclusive-NOR can be shown to be the complement of the exclusive-OR by means of a truth table or by algebraic manipulation: (x®y)=(xy'+x'y)'=(x'+y)(x+y')=xy+x'y' The following identities apply to the exclusive-OR operation: x®0=x x®1=x' x®x=0 x®x'=1 x®y'=x'®y=(x®y)' Any of these identities can be proven with a truth table or by replacing the e operation by its equivalent Boolean expression. Also, it can be shown that the exclusive-OR operation is both commutative and associative; that is, A®B=B®A and (A®B)®C=A®(B®C)=A®B®C This means that the two inputs to an exclusive-OR gate can be interchanged without affecting the operation. It also means that we can evaluate a three-variable exclusive-OR operation in any order, and for this reason, three or more variables can be expressed without parentheses. This
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