1- Implement (R = A O B) by using only NAND gates that two input, apply DeMorgan's theorems

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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O DA "l ZAIN IQ
В Lec5 Bool...
14
Digital Systems
Mustafa Al-Hashimi
EXI| Prove the relation is true :
ху+ху—ху +ху
SOL\\
Right hand side (RHS):-
x y +xy = x y.x y
DeMorgan's Theorem
= =
= (x + y)(x+y)
Rule 9: x = x
= (x + y)(x+y)
Factoring (distributive law)
= xx + x y + y x + yy
Rule 8: xx = 0, y y= 0
= x y + y x
Therefore the relation is true
Left hand side (LHS):-
ху+ху %3D ху.ху
Factoring (distributive law)
DeMorgan's Theorem
= (x + y) (x + y)
Rule 9: x =x
= (x+y) (x + y)
Factoring (distributive law)
= xx + xy+y x+ yy
Rule 8: xx = 0, y y= 0
= x y + y x
Therefore the relation is true
H.W//
1- Implement (R = A O B) by using only NAND gates that two input, apply
DeMorgan's theorems
15
Transcribed Image Text:O DA "l ZAIN IQ В Lec5 Bool... 14 Digital Systems Mustafa Al-Hashimi EXI| Prove the relation is true : ху+ху—ху +ху SOL\\ Right hand side (RHS):- x y +xy = x y.x y DeMorgan's Theorem = = = (x + y)(x+y) Rule 9: x = x = (x + y)(x+y) Factoring (distributive law) = xx + x y + y x + yy Rule 8: xx = 0, y y= 0 = x y + y x Therefore the relation is true Left hand side (LHS):- ху+ху %3D ху.ху Factoring (distributive law) DeMorgan's Theorem = (x + y) (x + y) Rule 9: x =x = (x+y) (x + y) Factoring (distributive law) = xx + xy+y x+ yy Rule 8: xx = 0, y y= 0 = x y + y x Therefore the relation is true H.W// 1- Implement (R = A O B) by using only NAND gates that two input, apply DeMorgan's theorems 15
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