Question

3. Harute wants you to write down the Formulation, Optimization, and Technology Mapping for the K-maps below: a. a.F (A, B, C, D) = ∑ m (2, 3, 5, 6, 9, 11, 13), d (A, B, C, D) = ∑ m (0, 1, 10, 12, 15) b. b.F (A, B, C, D) = ∏ M (5, 9, 10, 12, 15), d (A, B, C, D) = ∑ m (1, 8, 13, 14) c. c.F(A, B, C, D) = ∑ m (0, 1, 2, 3, 4, 12), d(A, B, C, D) = ∑ m (8, 9, 11, 10, 6, 14) - To make it more interesting, for the Technology Mapping is limited to using NAND gates only

Answer 1

a) F (A, B, C, D) = ∑ m (2, 3, 5, 6, 9, 11, 13), d (A, B, C, D) = ∑ m (0, 1, 10, 12, 15)

Above Function in K-map as follows

Simplified K-map as follows

The Simplified SOP of F (A, B, C, D) = A’B’+ABC’+AD+CD’+B’C+A’CD’

b) F (A, B, C, D) = ∏ M (5, 9, 10, 12, 15), d (A, B, C, D) = ∑ m (1, 8, 13, 14)

Above Function in K-map as follows

Simplified K-map as follows

The Simplified POS of F (A, B, C, D) =(A’+B’)(A’+D)(C+D’)

c) F(A, B, C, D) = ∑ m (0, 1, 2, 3, 4, 12), d(A, B, C, D) = ∑ m (8, 9, 11, 10, 6, 14)

Above Function in K-map as follows

Simplified K-map as follows

The Simplified POS of F (A, B, C, D) = BD