Question

Realize each of the following functions as a minimum two-level NAND-gate circuit and as a minimum two-level NOR-gate circuit.

(a) F(A,B,C,D) = BD′ + B′CD + A′BC + A′BC′D + B′D′


(b) f(a, b, c, d) = Π M(0, 1, 7, 9, 10, 13) · Π D(2, 6, 14, 15)


(c) f(a, b, c, d) = Σ m(0, 2, 5, 10) + Σ d(3, 6, 9, 13, 14, 15)


(d) F(A, B, C, D, E) = Σ m(0, 2, 4, 5, 11, 14, 16, 17, 18, 22, 23, 25, 26, 31) + Σ d(3, 19, 20, 27, 28)


(e) F(A, B, C, D, E) = Π M(3, 4, 8, 9, 10, 11, 12, 13, 14, 16, 19, 22, 25, 27)· Π D(17, 18, 28, 29)


(f ) f(a, b, c, d) = Π M(1, 3, 10, 11, 13, 14, 15) · Π D(4, 6)


(g) f(w, x, y, z) = Σ m(1, 2, 4, 6, 8, 9, 11, 12, 13) + Σ d(0, 7, 10, 15)

Answer 1

The creation of digital logic circuits using NAND and NOR gates for specified Boolean functions, a task common in digital electronics and computer engineering fields.

Step-by-step explanation:

The design of digital logic circuits using NAND and NOR gates based on given Boolean functions. The realization of two-level NAND and NOR gate circuits requires the understanding of Boolean algebra and the application of De Morgan's Theorems to convert the functions into a format that can be implemented using the desired gate types.

This problem is typical in the field of digital electronics and is relevant to disciplines like computer engineering and electronic engineering. Note that the given information includes both Sum-of-Products (SOP) and Product-of-Sums (POS) notation, as well as minterm and maxterm lists. To correctly design the circuits, each function must be transformed appropriately to be realized as NAND-only or NOR-only logic.