a)	Produce the Boolean expression equivalent to e in canonical sum of minterms form.
b)	Give a Karnaugh map for e and show the minimal set of prime implicants that covers e and the minimal set of prime implicants that covers e'.
c)	Produce a Boolean expression equivalent to e in each of the following standard forms: Minimum-literal sum of products Minimum-literal product of sums Minimum-literal inverted sum of products Minimum-literal inverted product of sums

Design a combinatorial circuit that implements the sum of minterms expression e = Sigma(1,2,3,...,14) using a 2-level XOR-OR circuit (XOR gates at level 1 and an OR gate at level 2).

In the following implementation of a full adder, show that the carry output (C) implements a three-input majority circuit.

A 4-bit increment-decrement circuit has 5 inputs (A₄, A₃, A₂, A₁, M) and 5 outputs (C₅, S₄, S₃, S₂, S₁), where A₄A₃A₂A₁, C₅, and S₄S₃S₂S₁ play the same role as in a 4-bit adder, and M selects that the sum S is obtained from the operand A by adding one (increment, M = 0) or subtracting one (decrement, M = 1). Implement a 4-bit increment-decrement circuit using a 4-bit full adder and inverters.

Consider the Boolean expression e = ((x'+z)'+y')'.

Analyze the following sequential circuit. Give a minimized Boolean expression for each circuit output and flip-flop input, a state table, and a state diagram showing all states.

Design a sequential circuit which implements the following state diagram using T flip-flops.