Please help with the following questions on Boolean expressions, K maps and circuts.

1. (20pts) Simplify each of the following Boolean expressions to a minimum number of literals using Boolean properties (a) A(A+ B) (B AA) (A B') (b) (A + C)(AD AD) + AC C (c) A(A + B'C) + A(B' C) (d) C+ (BC) 2. (8pts) Write a Boolean equation in sum-of-minterms form for each of the following truth tables A B C DY 0 0 00 1 0 0 01 0 0 0 1 0 1 0 0 11 1 0 1 0 0 0 0 1 01 0 0 1 1 0 1 0 1 1 1 1 A B C Y 0 11 1 1 0 01 1 0 10 1 1 01 1 0 10 1 0 1 0 1 1 0 1 1 0 1 1 00 0 1 1 01 0 1 1 1 0 0 3. (20pts) Use K-maps to minimize the Boolean equations in question 3, and draw the circuit for each simplified equation. 4. (31pts) Design a combination circuit with three inputs A, B, C (representing a 3-bit binary number, where A is the most significant bit, and C is the least significant bit), and three outputs X, Y, Z (representing a 3-bit binary number, where X is the most significant bit, and Z is the least significant bit). When the input is 0, 1, 2, or 3, the output is one greater than the input. When the input is 4, 5, 6, or 7, the output is one less than the input. For each of the output: (a) Construct the truth table and write the Boolean equation in sum-of-minterms form