ALJABAR BOOLEAN

1.Penyelesaian:

  =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/ +D ) + A/.B/.C (D + D/) + A.C.D/ (B+B/) + A.B/.C.D

=A/.B.C/ + AC (D/ +B/.D)

=A/.B/ +A/.D.C/ + AC (D/ + B/)

=A/(B/ +B.C/) +AC (D/ + B/)

=A/ (B/ + C/) + AC (D/ + B/)

=A/.B/ +A/.C/ +A.C.D/  +A.B/.C

2. Penyelesaian:

A/B/C/D/+A/BC/D/+AB/C/D/+A/B/CD+A/B/CD+A/B/CD/+A/BCD/+AB/CD/

AB/CD

=A/.C/.D/ (B/+B) + AB/.C./D/ +A/.B/.C. (D+D/)+CD/ (A/.B+A.B/) +AB/.C.D
=A/.C/.D/ + AB/.C/.D/ +A/B/C +CD/ (A/.B +A.B/) + A.B/C.D

=C/.D/ (A/ +A.B/) + B/.C (A/ +A.D) +C.D/ (A/.B +A.B/)

=C/.D/ (A/ + B/) +B/.C (A/ +D) +C.D/ (A/.B + A.B/)

=A/.C/.D/ + B/.C/.D/ +A/.B/.C + B/.C.D + A/.B.CD/ +A.B/.C.D/

=A/.D/ (C/ + B) + B/.C/.D/. + B/.C (A/ + D)

=A/.C/.D/ +A/.B.D/ + B/.C/.D/ + A/.B/.C + B/.C.D

 

3. Penyelesaian: A/B/C/+ABC/+AB/C/+A/B/C+AB/C

=A/.B/ (C/ +C ) +A.C/ (B+B/)

=A/.B/ +A.C/

   TUGA DIGITAL - ALJABAR BOOLEAN

   1.       X = ABC + A/.C    = C (AB + A/)

                                                 = C (A/ + B)

                                                 = A/.C +BC

    2.       Y = (Q + R) (Q/+R/)

=Q.Q/ + Q.R/ +Q/.R +R.R/

=Q.R/+Q/.R

    3.       W = ABC +A.B/.C + A/

=AC (B+B/) +A/

=AC +A/

=A/+C

    4.       Q = (RST)/.(R +S+ T)/

=R/ +S/ + T/. (R/.S/.T/)

=R/.S/.T/ + R/.S/.T/ + R/.S/.T/

    5.       X= A/.B/.C/ + A/.B.C +ABC+A.B/.C/+A.B/.C

=A/.B/.C/ + A.B/.C/ + A/.B.C + ABC +A.B/.C

=B/.C/ (A/+A) + BC(A/+A) + A.B/.C

=B/.C/ + BC + A.B/.C

=B/.C/ + C(B+A.B/)
=B.C/ + C(B+A)
=B.C/ + B.C+A.C

=B+AC

   6.       Z = ( B+C/).(B/+C) + A/+B+C)/

=B.B/+BC + B/.C/ + C.C/ +(A/.B/.C//)

=BC + B/.C/ +A.B/.C

=BC +B/ (C/+AC)

=BC + B/(C/+A)

=BC + B/.C/ +A.B/

   7.       Y= (C+D)/+ A/.C .D/ +A.D/.C/ +A/.B/.C.D + AC.D/

=C/.D/ +A/.C.D/ +AB/.C/ +A/.D/.CD + AC.D/

=C/.D/ +A/.C.D/ +AC.D/ + A.B.C/ + A/.B/.CD

=C/.D/ +C.D/ (A/+A) + B/(A.C/+A/.CD)

=D/ (C/+C) +C/A.C/ +A/.CD/)

=D/+AB/.C/+A/.B/.CD

   8.       X = AB(C/.D)/ + A/.B.D+B/.C/.D/

=AB(C+D/) +A/.BD +B/.C/.D/

=ABC+AB.D/ +A/BD +B/.C/D/

=ABC + A/BD + D/(AB +B/C/)

=B/(AC+A/D) + B/(AB +B/C/)

TUGAS ALARM

X= A.B/.C.D + A.B/.C.D + A.B/.C/.D + A/.B.C.D

=A.B/ (C.D + C/.D) + A/.B.C.D

=A.B/.D+A/.B.C.D

Pensederhanaan menggunakan teorema de'morgan

a)  A// . B/ . C//                    =  A . B/ . C

                                     A + B/ + C

b)  A// + (B// . C/)               =  A + (B . C/)
                                               A . (B + C/)
                                               (A . B) + (A . C/)

c)  A/ . B/ . C// . D//            =  A/ . B/ . C . D
                                               A/ + B/ + C + D

d)  A/ + B//                         =  A/ + B
                                               A/ . B

e)  A// . B//                          =  A . B
                                                A + B

f)  A// + C// + D//                =  A + C + D
                                               A . C . D

g)  A/ . (B// + C///) . D/       =  A/ . (B + C/) . D/
                                               A/ + (B . C/) + D/

h)  (M/ + N//) . (M// + N/)   =  (M/ + N) . (M + N/)
                                               (M/ + N) . (M + N/)
                                               (M/ . N) + (M . N/)

    i)    A/// . B/// . C// . D/         =  A/ . B/ . C . D/

                                               A/ + B/ + C + D/