Question

***PLEASE EXPLAIN EACH STEP CLEARLY. THANK YOU Simplify the Boolean expression: a.b’.c’.d + a.b’.c.d + a.b.c’.d...

***PLEASE EXPLAIN EACH STEP CLEARLY. THANK YOU

Simplify the Boolean expression: a.b’.c’.d + a.b’.c.d + a.b.c’.d + a.b.c.d’ + a.b.c.d

Answers:

A. a.b.c + a.b.d + b.c.d

B. a.c + a.b.d

C. a.c + b.d + b.c

D. can’t be simplified

E. a.d + a.b.c

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Homework Answers

Answer #1

a.d + a.b.c

EXPLANATION

a.b’.c’.d + a.b’.c.d + a.b.c’.d + a.b.c.d’ + a.b.c.d
a.b’.c’.d + a.b’.c.d + a.b.c’.d + a.b.c.d’ + a.b.c.d + a.b.c.d + a.b.c.d
a.b’.c’.d + a.b’.c.d+ a.b.c.d + a.b.c’.d+ a.b.c.d + a.b.c.d’ + a.b.c.d
a.b’.c’.d + a(b’+b)c.d + a.b(c’+c)d + a.b.c.(d + d')
a.b’.c’.d + a(1)c.d + a.b(1)d + a.b.c.(1)
a.b’.c’.d + a.c.d + a.b.d + a.b.c
a(b’.c’.d + c.d + b.d + b.c)
a((b’.c’ + c)d + b.d + b.c)
a((b’ + c)d + b.d + b.c)
a(b’d + c.d + b.d + b.c)
a(b’d + c.d + b.d + b.c)
a(c.d +(b' + b)d + b.c)
a(c.d +(1)d + b.c)
a(c.d + d + b.c)
a(d + b.c)
a.d + a.b.c

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