please show as much work as possible!

PROBLEM 3 (11 PTS) We want to design a logic circuit that opens a lock (Q = 1) whenever the user presses the correct number on each numpad (numpad 1: 8, numpad2: 3). The numpad encodes each decimal number using BCD encoding (see figure). We expect that the 4-bit groups generated by each numpad be in the range from 0000 to 1001. Note that the values from 1010 to 1111 are assumed not to occur. Provide the simplified expression for Q(a, b, c, d, e, f, g, h) and sketch the logic circuit. Suggestion: Create two circuits: one that verifies the first number (8), and another that verifies the second number (3). Then perform the AND operation on the two outputs. This avoids creating a truth table with 8 inputs. BCD code Number pressed X Y Z W o caoO OU ? e 1 2 3 2 3 4 5 6 XVZW - N 0 0 - 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 O ooo N 8 9 2 3 5 6 4 5 6 Numpad 1 8 9 0 Numpad 2 PROBLEM 4 (26 PTS) a) Complete the timing diagram of the following circuit: (5 pts) 11 H 1 1 11 0 F LE b E 1 1 f E 1 . 1 f 1 1 b) Complete the timing diagram of the logic circuit whose VHDL description is shown below: (7 pts) library ieee; use ieee.std_logic_1164.all; 11 1 1 1 entity cire is port (a, b, c: in std logic; f: out std logic) ; end circ; 1 architecture struct of circ is signal x, y: std logic; 1 begin f