📜  门| GATE-CS-2015(套装2)|第 47 题

📅  最后修改于: 2021-09-27 05:26:30             🧑  作者: Mango

最小化以下布尔表达式后的最小项数是_________。

[D′ + AB′ + A′C + AC′D + A′C′D]′

(一) 1
(乙) 2
(三) 3
(四) 4答案:(一)
解释:

Given Boolean expression is: 
              [D′ + AB′ + A′C + AC′D + A′C′D]′

Step 1 : [D′ + AB′ + A′C + C′D ( A + A')]′ 
( taking C'D as common )

Step 2 : [D′ + AB′ + A′C + C′D]′ 
( as, A + A' = 1 )

: [D' + DC' + AB' + A'C]' (Rearrange)

Step 3 : [D' + C' + AB' + A'C]' 
( Rule of Duality, A + A'B = A + B )

: [D' + C' + CA' + AB']' (Rearrange)

Step 4 : [D' + C' + A' + AB']' 
(Rule of Duality)

: [D' + C' + A' + AB']' (Rearrange)

Step 5 : [D' + C' + A' + B']' 
(Rule of Duality)

:[( D' + C' )'.( A' + B')'] 
(Demorgan's law, (A + B)'=(A'. B'))

:[(D''.C'').( A''.B'')] (Demorgan's law)

:[(D.C).(A.B)] (Idempotent law, A'' = A)

: ABCD

Hence only 1 minterm after minimization. 

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