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in Digital Logic 60 views
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Is it C?
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Yes please tell in detail
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We should know that an expression in POS form is always easier to be realized by NOR gates.

Given is the SOP ∑m(0,2,6,10,14) so we should convert it to POS.

Hence piM(1,3,4,5,7,8,9,11,12,13,15) [I couldn't find the "pi" symbol :P]

So the expression is D'.(B'+C).(A'+C)

Now we have to convert this expression in such a way that we can realize it with NOR

( ( D'.(B'+C).(A'+C) )' )' = (  (D')' + (B'+C)' + (A'+C)' )' = (D + BC' + AC' )'

= (D + C'(A+B) )' = (  D + ( ( C'(A+B) )' )'   )' = (D + ( (C')' + (A+B)' )' )' 

= (D + ( C + (A+B)' )' )' 

X=(A+B)'  --> 1 NOR

Y=(C+ X)'  --> 1 NOR

(D+Y)' --> 1 NOR

2

By k-map, SOP format ===> CD' + A' B' D' ===> D' (C+A'B') ==> D' . ( C + (A+B)' ) ===> ( D + ( C + (A+B)' )'  ) '

TOTAL = 3 NOR GATES

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Yeah.. Shaik's one is faster.. usually converting to POS works better..but in this case it's not

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