#1 and #2

The truth table for Boolean expression is shown below. Write the Boolean expression in sum of-products form. 1. 0 1 0 0 1 0 1 0 2. Given the Boolean function F(x,yz)-x'yxyz' a) Derive an algebraic expression for the complement of F. Express in sum-of-products form b) Show that FF 0. c)Show that F+F-1 3. Design a circuit with three inputs (x, y, and z) representing the bits in a binary number, and three outputs (a, b, and c) also representing bits in a binary number. When the input is 1, 2, or 3, the binary output should be one lesser than the input. When the input is 4, 5, or 6, the binary output should be one greater than the input. When the input is 0, the output is 0, and when the input is 7, the output is 7. Show your truth table, all computations for simplification, and the final circuit