3.29 T he following circuit is implemented using two half-adder circuits. The expressions for the half-adder outputs are S A田B, and C = AB. Derive simplified sum-of- products expressions for the circuit outputs SUM and Co. Give the truth table for the outputs. SUM B C B C Co

Using Boolean Algebra, simplify the following logical expression? (You may use K- map) F = XY + X (Y+ Z) + Y(Y+Z)

Using elementary rules of Boolean algebra, find the simplest equivalent of the Boolean expressions below using only products, sums, and negation (i.e., no XOR). Show your derivation step by step. Label each step with the name of the rule you apply.

Draw a logic diagram that implements the Boolean expression of ((x'+y)y)'.