Question

Could you show me how to form PLAs for the following question? Thanks.

7. Draw a PLA for the following functions, given in S notation, using variables x₀, x₁, x₂, x₃.

1. f₁ = S (0, 3, 5, 7, 8, 11, 13)
2. f₂ = S (1, 2, 3, 6, 11, 13, 14, 15)
3. f₃ = S (0, 2, 4, 6, 7, 12, 13, 15)
4. f₄ = S (1, 4, 5, 6, 9, 10, 12)
5. f₅ = S (2, 3, 4, 5, 8, 9, 10, 11, 14)

Answer 1

Given Function is

f1 (x0, x1, x2, x3) =m (0, 3, 5, 7, 8, 11, 13)

f2 (x0, x1, x2, x3) =m (1, 2, 3, 6, 11, 13, 14, 15)

f3 (x0, x1, x2, x3) =m (0, 2, 4, 6, 7, 12, 13, 15)

f4 (x0, x1, x2, x3) =m (1, 4, 5, 6, 9, 10, 12)

f5 (x0, x1, x2, x3) =m (2, 3, 4, 5, 8, 9, 10, 11, 14)

m0 = 0000 = xo'x1'x2'x3'

m1 = 0001 = xo'x1'x2'x3

m2 = 0010 = xo'x1'x2x3'

m3 = 0011 = xo'x1'x2x3

m4 = 0100 = xo'x1x2'x3'

m5 = 0101 = xo'x1x2'x3

m6 = 0110 = xo'x1x2x3'

m7 = 0111 = xo'x1x2x3

m8 = 1000 = xox1'x2'x3'

m9 = 1001 = xox1'x2'x3

m10 = 1010 = xox1'x2x3'

m11 = 1011 = xox1'x2x3

m12 = 1100 = xox1x2'x3'

m13 = 1101 = xox1x2'x3

m14 = 1110 = xox1x2x3'

m15 = 1111 = xox1x2x3

PLA:

Explanation:
Negation(¬) of any logical Identity P is Nothing but Opposite Truth Value for P. i.e If P is T then (¬P) is F
And gate is used to find the Product of Two literals P AND Gate Q Output is PQ
OR gate is used to find the Sum of Two literals P OR Gate Q Output is P+Q