Question

1.) what is the correct number of terms and literals for each of the following functions: (DO NOT COUNT DON'T CARES INTO TERMS AND LITERALS)

a.) Z(A,B,C,D,E,F)= Σm(1,3,4,5,9,11,16,18,20,27,31,32,36,40,45,46,47,49,50,52,54,59,61,62) +Σd(0,2,6,8,23,34,53,63)

b.) F(A,B,C,D)= A'B'C'D' + ABC'D'+ A'BCD' + AB'CD +A'BC'D +A'BCD

c.) F(A,B,C,D)= Σm (0,2,8,10,13,15)+Σd (5,7)

d.) F = B'D' + ABD

e.) F= (B+D')(B'+D)(A+D')

f.) F= A'B'C'D' + ABC'D' + A'BC + AB'D + A'BD

g.) F = (A'+ B'+ D') (A'+ B + D ) (A + B'+ C + D ) (A + B + D') (A'+ C'+ D ) (A + B + C')

h.) Z= (A'+B'+D+E+F)

i.) B C E F + A B C'E'F + A C D E + A C D F + B'D'E'F' +A'B'C'E' + A B C'E F' + C'D E'F' + A'B'D'F + A'C'D'F'

Answer 1

For an 'n' variable function,we have a total of2n literals.

eg.F(A,B) we have '2' variables A and B ,and hence we have a total of 2n=2*2=4 literals namely A,A',B AND B'.

An expression may have all or only a part of the literlas in it.eg. in F(A,B)=A' + B , we only have just 2 literals included out of the total 4.

since the question is finding out the number of literals in an expression we only need to find the number of times each literal occurs in the expression .

The number of terms are basically the number of terms in the given expression.i.e it the number of POS(product of sum) or SOP(sum of products)

1)Z(A,B,C,D,E,F)=m(1,3,4,5,9,11,16,18,20,27,31,32,36,40,45,47,49,50,52,54,59,61,62) +d(0,2,6,8,23,34,53,63)

ANSWER: the given function has 24 terms each having 6 variables(excluding the dont count conditions)

hence the total number of terms 24*6=144 literals.

b)F(A,B,C,D)=A'B'C'D'+ABC'D'+A'BCD'+AB'CD+A'BC'D+A'BCD

ANSWER: number of terms =6

since each term has 4 literals we have a total of 6*4=24 literals.

c)F(A,B,C,D)=m(0,2,8,10,13,15) +D(5,7)

ANSWER: Number of valid terms =6 terms

and with each term having 4 variables(A,B,C,D) we have total literals=6*4=24 literals

D)F=B'D'+ABD

ANSWER: number of terms in expresson=2 terms

total number of literals in thw function =2(B'D')+3(ABD)= 5 literals.

E)F=(B+D')(B'+D')(A+D')

ANSWER: number of terms=3 terms

number of literals= 2+2+2=6 literals

F)F=A'B'C'D'+ABC'D'+A'B'D+A'BD

ANSWER: number of terms=4 terms

number of literals=4+4+3+3=14 literals

G)F=(A'+B'+D')(A'+B+D)(A+B'+C'+D)(A+B+D')(A'+C'+D)(A+B+C')

ANSWER: number of terms=6 terms

number of literals=3+3+4+3+3+3=19 terms

H) Z=(A'+B'+D+E+F)

ANSWER: number of terms=1

number of literals=5 literals.

I)BCEF+ABC'E'F+ACDE+ACDF+B'D'E'F+A'B'C'E'+ABC'EF'+C'DE'F'+A'B'D'F+A'C'D'F'

ANSWER: total number of terms= 10 terms

total number of literals=4+5+4+4+4+4+5+4+4+4=42 literals.

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hope my answer was helpful.