Question

1.) Simplify the following Boolean Expression to a minimum number of literals.

(a'b' + c)(a + b + c')

a.)ab + a'b'c' + ac

b.)ac + abc + bc

c.)ac + a'b'c' + bc

d.)a'c + abc + b'c

e.)None of the above

2.) Reduce to two literals.

wxy'z + w'xz + wxyz

a.) xz

b.) x'z

c.) xz'

d.) yz

e.) None of the above

Answer 1

Solution:

(1)

Given,

=>Expression = (a'b' + c)(a + b + c')

The answer will be an option,

(c) ac + a'b'c' + bc

Explanation:

Simplification of expression:

=>Expression = (a'b' + c)(a + b + c')

Multiplying both terms

=>Expression = a'b'a + a'b'b + a'b'c' + ca + cb + cc'

=>Expression = a'ab' + ab'b + a'b'c' + ac + bc + cc'

We know that a'a = 0, b'b = 0 and cc' = 0

=>Expression = 0.b' + a.0 + a'b'c' + ac + bc + 0

=>Expression = a'b'c + ac + bc

=>Hence on the basis of simplified expression option (b) is correct and other options are incorrect.

(2)

Given,

=>Expression = wxy'z + w'xz + wxyz

The answer will be an option,

(a) xz

Explanation:

Simplification of expression:

=>Expression = wxy'z + w'xz + wxyz

Taking wxz common from first and third terms

=>Expression = wxz(y' + y) + w'xz

We know that y' + y = 1

=>Expression = wxz + w'xz

Taking xz common from first and second terms

=>Expression = (w + w')xz

We know that w + w' = 1

=>Expression = xz

=>Hence on the basis of simplified expression option (a) is correct and other options are incorrect.

I have explained each and every part with the help of statements attached to it.