Question

design a half adder and a full adder following the logic circuit design process starting with their truth table. please provide their boolean equations and their schematic gate-level circuit. the detailed steps are needed (hint: you want to follow the steps of logic circuit design like identifying inputs/outputs, building truth table, etc.)

Answer 1

A half adder is a digital circuit that adds two single-bit binary numbers. The boolean equations for a half adder are: Sum = A XOR B and Carry = A AND B.

Step-by-step explanation:

Half Adder

A half adder is a digital circuit that adds two single-bit binary numbers without considering any carry input. It has two inputs, A and B, and two outputs, Sum and Carry. A full adder is a digital circuit that adds two single-bit binary numbers along with a carry input. The boolean equations for a full adder are: Sum = A XOR B XOR Cin and Cout = (A AND B) OR (Cin AND (A XOR B)). The truth table and boolean equations for a half adder are as follows:

ABSumCarry0000011010101101

The boolean equations for the outputs of a half adder are: Sum = A XOR B and Carry = A AND B.

The schematic gate-level circuit for a half adder is shown below:

Full Adder

A full adder is a digital circuit that adds two single-bit binary numbers along with a carry input. In addition to the inputs and outputs of a half adder, a full adder also has a carry input Cin. The truth table and boolean equations for a full adder are as follows:

ABCinSumCout0000000110010100110110010101011100111111

The boolean equations for the outputs of a full adder are: Sum = A XOR B XOR Cin and Cout = (A AND B) OR (Cin AND (A XOR B)).