![(a) f(A, B,C,D)= [A + (BCD)][(AD), + B(C, + A)] (b) f(A, B,C,D) = AB,C + (A + B + D)(AB D + B)](https://d2vlcm61l7u1fs.cloudfront.net/media%2F80b%2F80b7b291-0bfa-41f3-b193-78dc0941a052%2FphpreeoQD.png)
Use DeMorgan’s Law and Involution Law to experience the fulfilment of the discharges
please demonstration each step! i dont amply comprehend..
(a) f(A, B,C,D)= [A + (BCD)’][(AD), + B(C, + A)] (b) f(A, B,C,D) = AB,C + (A’ + B + D)(AB D’ + B’)
a)
f(A,B,C,D) = [A + (BCD)’][(AD)’ + B(C’ + A)]
fulfilment of the discharge :
f’ (A,B,C,D) = ([A + (BCD)’][(AD)’ + B(C’ + A)])’
f’ (A,B,C,D) = [A + (BCD)’]’ + [(AD)’ + B(C’ + A)]’
f’ (A,B,C,D) = ((A’ ) (BCD)) + ((AD) (B’+(C’+A)’))
f’ (A,B,C,D) = (A’BCD) + ((AD)(B’+(CA’))
f’ (A,B,C,D) = (A’BCD) + (AB’D + AA’CD)
f’ (A,B,C,D) = A’BCD + AB’D
b)
f(A,B,C,D) = AB’C + (A’ + B + D)(ABD’ + B’)
fulfilment of the discharge ——->
f'(A,B,C,D) = (AB’C + (A’ + B + D)(ABD’ + B’))’
f'(A,B,C,D) = (AB’C)’ ((A’ + B + D)(ABD’ + B’))’
f'(A,B,C,D) = (A’ + B + C’) ((A’ + B + D)’ + (ABD’ + B’)’)
f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + ((ABD’)’ (B’)’))
f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + ((A’+B’+D)(B)))
f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + ((A’B+BB’+BD)))
f'(A,B,C,D) = (A’ + B + C’) ((AB’D’) + (A’B + BD))
f'(A,B,C,D) = AA’B’D’ + A’A’B + A’BD + ABB’D’ + A’B + BD + AB’C’D’ + A’BC’ + BC’D
f'(A,B,C,D) = A’B + A’BD + A’B + BD + AB’C’D’ + A’BC’ + BC’D
f'(A,B,C,D) = A’B(1+D+1+C’)+BD(1+C’)+AB’C’D’
f'(A,B,C,D) = A’B + BD + AB’C’D’