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212 Fundamentals of Computers NPP

3.24 Logical Circuit Design 3.24 Vm{H©$H$ n[anWm| H$s ga§MZm
Logic circuit is a circuit containing Logic {OZ n[anWm| _| Vm{H©$H$ JoQ> hmoVo h¢ CÝh| Vm{H©$H$
gates. Any Boolean function can be imple- n[anW H$hVo h¢Ÿ& {H$gr ^r ~y{b`Z \$bZ H$m Vm{H©$H$
mented using a logic circuit. Many logic gates n[anW ~Zm`m Om gH$Vm h¡Ÿ& {H$gr ^r Vm{H©$H$ n[anW
are interconnected in a logic circuit to provide _| ~hþV go JoQ> Bg Vah go Omo‹S>o OmVo h¢ {H$ BZnwQ> d
the relationship between inputs and outputs.
This relationship may also be obtained from AmCQ>nwQ> _| Mmho JE g§~§Y àmá {H$E OmEŸ& `hr g§~§Y
truth tables. Basically, there are two types of gË`Vm{bH$m go ^r kmV hmoVm h¡Ÿ& Vm{H©$H$ n[anW Xmo
logic circuits: àH$ma Ho$ hmoVo h¢ …
1. Combinational Logic Circuit 1. H$m§{~ZoeZb Vm{H©$H$ n[anW
2. Sequential Logic Circuit 2. {gŠdoÝeb Vm{H©$H$ n[anW
Combinational Logic Circuit H$m§{~ZoeZb Vm{H©$H$ n[anW
In this logic circuit the present outputs are Bg àH$ma Ho$ Vm{H©$H$ n[anW _| dV©_mZ AmCQ>nwQ>
obtained from the present inputs. The output is dV©_mZ BZnwQ> na {Z^©a H$aVo h¢Ÿ& `o AmCQ>nwQ> n[anW
independent from the previous conditions of H$s nwamZr AdñWmAm| na {Z^©a Zht H$aVoŸ& g^r àH$ma
the circuit. All gates are combinational in nature,
because the output of gate can be seen from the Ho$ JoQ> H$m§{~ZoeZb hmoVo h¢ Š`m|{H$ BZ_| BZnwQ> H$mo XoIVo
inputs. The examples of combinational logic go hr AmCQ>nwQ> ~Vm`m Om gH$Vm h¡Ÿ& Xygao CXmhaUm| _|
circuits are Half Adder, Full Adder, Multiplexer, {ZåZ à_wI h¡ ; hm\$ ES>a, \w$b ES>a, _pëQ>ßboŠga,
Demultiplexer, Decoder, Encoder etc. {S>_pëQ>ßboŠga, {S>H$moS>a, EÝH$moS>a Am{XŸ&

Sequential Logic Circuit {gŠdoÝeb Vm{H©$H$ n[anW
Sequential logic circuits can be defined as Bg àH$ma Ho$ Vm{H©$H$ n[anW _| dV©_mZ AmCQ>nwQ>,
the interconnection of gates in which the present n[anW H$s nwamZr pñW{V VWm dV©_mZ BZnwQ> XmoZm| na
output depends upon the previous conditions {Z^©a H$aVo h¢Ÿ& CXmhaUV… pâbn-âbm°n, a{OñQ>a VWm
of the circuit. Examples of sequential logic H$mC§Q>aŸ&
circuits are flip-flops, Registers, counters etc.
Problem 3.59 àíZ 3.59
Draw the Karnaugh map for the follow- {ZåZ Vm{bH$m hoVw K-_on ~ZmAmo:
ing truth table:
A B Y
0 0 1
0 1 0
1 0 0
1 1 1
Solution: hc:
The Karnaugh map gives the same infor- K-_on dhr OmZH$mar àXmZ H$aVm h¡ Omo gË` Vm{bH$m
mation as provided by the truth table. The two àXmZ H$aVr h¡Ÿ& Xmo am{e`m| H$m K-_on {ZåZmZwgma ~Zm`m
variable Karnaugh map would be drawn as fol-
lows: Om gH$Vm h¡: