Question

How to simplify the following expression : A'BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD ? It should get AC + BCD + ABD using Kmap but using boolean algebra i am stuck no matter how i try .

Answer 1

u know what is A+A' = ?

Answer 2

yes , it is 1

Answer 3

so A'BCD+ABCD = ?
first term + last term

Answer 4

A'BCD + ABCD = BCD ( A' + A ) = BCD

Answer 5

correct,
A'BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD

i would also add ABCD (i can because ABCD+ABCD=ABCD , right ? )
A'BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD + ABCD
= BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD

got this ?
now ABCD+ABC'D = ?

Answer 6

Yes , I got the first one
ABD ( C + C' ) = ABD

Answer 7

so now only , AC remains...let me see.....

Answer 8

i think we need one more ABCD
A'BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD + ABCD+ABCD
= BCD + ABD + AC (B'D+BD' + BD+B'D')

Answer 9

so now we just need to prove (B'D+BD' + BD+B'D')=1

Answer 10

can u prove (B'D+BD' + BD+B'D')=1
?

Answer 11

and did u get this :
A'BCD + AB'CD' + AB'CD + ABC'D + ABCD' + ABCD + ABCD+ABCD
= BCD + ABD + AC (B'D+BD' + BD+B'D')
?

Answer 12

i am trying to prove it ,,, n yes i got what u did so far ..

Answer 13

yes it is 1

Answer 14

(B'D+BD' + BD+B'D')=1
proving that is pretty simple, ask if u don't get it...

Answer 15

hint : take 1st and 3rd term..... 2nd and 4th term..

Answer 16

no no i can do it ... D ( B' + B ) + D' ( B' + B ) then D + D' = 1

Answer 17

good !

Answer 18

so clear with all steps ?

Answer 19

the trick here was to add ABCD twice and use it..

Answer 20

Yeah I was stuck becz i didn't think of adding ABCD twice and only tried to simplify with the existing ones..
Thank you soooooo much :) You are way better than my teacher ,,, by explaining easily step by step I understood really well :) Thank you so much :) You are really a lifesaver :)

Answer 21

welcome ^_^
glad i could help :)