Design a combinational logic circuit for 4-input majority circuit

Design a combinational logic circuit for 4-input majority circuit. A majority circuit is one which produces a HIGH (1) output when three or more inputs are high (1).

i. Construct the truth table and simplify the Boolean expression into SOP and POS forms using K-map.

ii. Construct the logic diagram using AND-OR gate network with simplified SOP expression.

iii. Construct the logic diagram using OR-AND gate network with simplified POS expression.

iv. Construct the logic diagram using only NAND gates with simplified SOP expression.

v. Construct the logic diagram using only NOR gates with simplified POS expression.