Digital teknique

4-1.        SIMPLIFY WITH ALJABAR BOOLEAN

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

B.       Y = (Q + R) (Q/+R/)

        =Q.Q/ + Q.R/ +Q/.R +R.R/

        =Q.R/+Q/.R

C.    W = ABC +A.B/.C + A/

          =AC (B+B/) +A/

          =AC +A/

          =C + A/

D.    Q = (RST)/.(R +S+ T)/

          =R/ +S/ + T/. (R/.S/.T/)

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

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

        =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

F.      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/

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

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

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

           =D/(C+D) B/

           =D/C.B/

H.   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) + D/(AB +B/C/)

4-6 

A manufacturing plant needs to have a horn sound signal quitting time. the horn sound should be activated when either the following is met.

1. it's after 5 o'clock and all machines are shut down

2. it's Friday, the production run for day is complete, and all machines are shut down

design the logic circuit that will control the horn (hint: use for logic input variables to represent the various conditions. for examples input A will be high only when  the time of the day is 5 o'clock or later..

ANSWER :

A = 5 O'CLOCK

B = MACHINES ARE SHUT DOWN

C = FRIDAY

D = PRODUCT IS COMPLETES

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

SOAL 4-49

1.      A/B/C/D/ + A/B/C/D + A/B/CD + A/B/CD/ + A/BC/D/ + A/BC/D + ABCD/ + AB/CD + AB/CD/

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

=A/B/(C/+C) + A/BC/ + ABCD/ + AB/C

=A/B/+A/BC/+ABCD/+AB/C

=A/(B/+BC/) + ABCD/ + AB/C

=A/(B/+C/) +ABCD/ + AB/C

=A/B/+A/C/+ABCD/+AB/C

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

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

=B/A/ + B/C + A/C/ + ABCD/

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

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

       =A/B/(1+CD/)+ABD/+AB/(1+CD/)

       =A/B/+A/B/CD/+ABD/+AB/(1+CD/)

       =A/B/+A/B/CD/+ABD/+AB/+AB/CD/

       =B/(A/+A/CD/)+A+ACD/)+ABD/

       =B/(1+CD)+ABD/

       =B/+B/CD+ABD/

       =B/+ABD/

3. A/B/C+A/B/C+ABC/+AB/C/+AB/C
   =C/(A/B/+AB+AB/)+C(A/B/+AB/)
   =C/(1+AB/)+CB/
   =C/+C/AB/+CB/
   =C/+B/(C/A+C)
   =C/+B/(C+A)
   =C/+B/C+B/A
   =C/+B/C+B/A
   =C/+B+B/A
   =C/+B+A