[SOLVED] BLG 231E - Digital Circuits Assignment 3

The function 𝑓(𝑎, 𝑏, 𝑐, 𝑑) is given below:

f(𝑎, 𝑏, 𝑐, 𝑑) = ∪₁(0, 2, 4, 5, 8, 10, 11, 13, 15) + ∪_Φ (1, 6)

1. Find the set of all prime implicants using the two different methods below:

1. A Karnaugh map.
2. The Quine-McCluskey method (Sort the minterms into groups according to the number of 1’s in each term. Compare pairs of terms in adjacent groups and combine terms where possible. Check off terms which have been combined.)

2. Construct the prime implicant chart using the cost criteria given below, then simplify the chart to identify all essential prime implicants. Show and explain each step of the simplification. Write out the expression for the function with the lowest cost, and give the total cost.

Cost criteria: 2 units for each variable and 1 unit for each complement sign.