# 逻辑代写/数学代写/math代写 – CPS250 logic

Due: March 15, 2018

1. A combinational circuit produces the majority vote for three one-bit inputs. Whenever at least two of the inputs are one, the output become one. The inputs are x1, x2, and x3; and the output is z.

a) Provide a truth table of the combinational circuit.

b) Write the Boolean equation.

c) Simplify the Boolean equation using K-map.

d) Draw the logic diagram

2. Construct a 2×4 decoder.

a) Provide a truth table of the combinational circuit.

b) Write the Boolean equations.

c) Draw the logic diagram

3. Construct a 4×1 input Muliplexer.

a) Provide a truth table of the combinational circuit.

b) Write the Boolean equations.

c) Draw the logic diagram

4. Derive the carry input C5 for a 5-bit carry lookahead adder in terms of g, p, G, and P.

Assume that the numbers are represented as x4x3x2x1x0 and y4y3y2y1y0, and carry in as C0.

Note: writing only the equation is not enough; you should show all the steps for obtaining such an equation.

5. Draw the NAND logic diagram for the following expression using multiple-level NAND gate circuit:

F(A,B,C,D,E) =AB’ + C’D’ + BC’ (A + B)

6. Construct an 8×1 multiplexer with two 4×1 and one 2×1 multiplexers. Use block diagrams for the three multiplexers. Label all the inputs of the multiplexers.