Page 304 - FUNDAMENTALS OF COMPUTER

NPP

304 Fundamentals of Computers NPP

{H$gr ~mBZar g§»`m H$s no[aQ>r H$s Om§M H$aVm h¡Ÿ& `{X `h g_ h¡ Vmo AmCQ>nwQ> no[aQ>r MoH$a
1 AmVm h¡ VWm {df_ h¡, Vmo AmCQ>nwQ> eyÝ` AmVm h¡Ÿ& d OZaoQ>a
3.39 Implementation Using NAND and 3.39 `y{Zdg©b JoQ>m| H$s ghm`Vm go Bpåßb_|Q>oeZ
NOR gates (Universal Gates) (NAND VWm NOR go)

NAND and NOR gates are called univer- NAND VWm NOR JoQ> H$mo `y{Zdg©b JoQ> H$hVo
sal gates because any logic circuit can be imple- h¢, Š`m|{H$ BZ_| go {H$gr EH$ H$s ghm`Vm go {H$gr ^r
mented using NAND gates only. The same logic
circuit may be implemented using NOR gates Vm{H©$H$ n[anW H$mo ~Zm`m Om gH$Vm h¡Ÿ& `h B§{Q>J«oeZ
only. The NAND-NAND and NOR-NOR imple- VH$ZrH$s _| Cn`moJ _| AmVm h¡Ÿ& Š`m|{H$ Eogm H$aZo na
mentation is used in Integration technology. Be- gånyU© {Mn Ho$ AÝXa EH$ hr àH$ma Ho$ noQ>Z© àmßV {H$E
cause when the circuit is in this form the same
pattern of the universal gate may be used OmVo h¢ d ~mX _| BÝh| d¥hX ñVa na ~Zm`m
through the circuit. OmVm h¡Ÿ&
There are four important equivalence `y{Zdg©b JoQ>m| go {H$gr n[anW H$mo ~ZmZo Ho$ {bE
which are used while performing implementa- Mma _hËdnyU© ~mVm| H$m Ü`mZ aIZm hmoVm h¡, Omo Bg
tion using universal gates :
àH$ma h¢…
1. NAND gate is equivalent to Bubbled OR 1. NAND JoQ> Vwë` hmoVm h¡, ~~ëS> OR JoQ> Ho$Ÿ&
gate.
2. NOR gate is equivalent to bubbled AND 2. NOR JoQ> Vwë` hmoVm h¡, ~~ëS> AND JoQ> Ho$Ÿ&
gate.
3. Shorted NOR gate is equivalent to NOT 3. em°Q>}S> NOR JoQ> Vwë` hmoVm h¡, NOT JoQ> Ho$Ÿ&
gate.
4. Shorted NAND gate is equivalent to NOT 4. em°Q>©oS> NAND JoQ> Vwë` hmoVm h¡, NOT JoQ> Ho$Ÿ&
gate.
Let us prove one by one: A~ BÝh| EH$-EH$ H$aHo$ g_PVo h¢:
1. The output of a NAND gate after applying 1. NAND JoQ> Ho$ AmCQ>nwQ> H$mo {S>-_m°J©Z H$m {Z`_
DeMorgan’s Theorem can be written as: bJmZo Ho$ níMmV² Bg àH$ma go {bIm Om gH$Vm h¡…

A
B A.B = A + B
The output of Bubbled OR gate is: gmW hr ~~ëS> OR JoQ> Ho$ AmCQ>nwQ> H$mo ^r Bg
àH$ma go {bIm Om gH$Vm h¡…

A

B A + B

Thus, both the gates produce same output AV… ñnîQ> h¡ {H$ XmoZm| ì`§OH$ EH$X_ g_mZ h¢Ÿ&

A + B .