Q1: A “black box” has an output value of “1” if there are more 1’s than 0’s on its inputs. The output is “0” otherwise. To design this 3-input function with inputs A, B, C, and output F:

a- Generate a truth table (10 points).

b- With a K-map, generate a reduced SoP equation for the output (10 points).

Q2: Simplify the binary equation below (10 Points). Draw the logic circuit (10 points).

F = x.y + x’.z + x’.y.z + x.y.z

Q3: Given the following logic equation. Implement it using a ‘153 mux.

Mark pins, signals and components correctly. All signals are active-high. (15 points).

F= a’.q’.t.z + a.q.z.w + a.q’.t + a.q.t.w

Q4: Draw timing diagram on the given circuit below, indicate transitions of output “Out”. Show your work clearly please.

(15 points)

Info: All Positive Edge Triggered Flip Flops.

Q5: Total Question value is 15 points.

Draw the state transition diagram for a MOORE state machine that would detect the sequence of “ 0011”. Name states A,

B, C, D, E, ….. Use minimum number of states. This is a Non overlapping machine.

(a) First show how output would look like below (3 points):

Input: x = 0 0 1 0 1 1 0 1 0 0 1 1 0 1 0 1 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0

Output: f = _________________________________________________________

(b) Draw state transition diagram below(10 points):

Q6: Design a Shift register using D Flip-Flops, to detect incoming bit sequence of “01101”. Show your work clearly

please. (15 points)