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

To design a half adder and full adder, you need to follow the steps of logic circuit design including identifying inputs/outputs, building truth table, writing boolean equations, and designing gate-level circuits.

Step-by-step explanation:

Designing a Half Adder

1. Identify the inputs and outputs: The inputs for a half adder are A and B (the two bits to be added), and the outputs are Sum (the sum of A and B) and Carry (the carry out bit).
2. Build the truth table: The truth table for a half adder will have 4 rows, representing the possible combinations of inputs and their corresponding outputs.
3. Write the boolean equations: Based on the truth table, you can write the boolean equation for the Sum output as Sum = A'B + AB', and for the Carry output as Carry = AB.
4. Design the gate-level circuit: The gate-level circuit for a half adder consists of an XOR gate for the Sum output and an AND gate for the Carry output.

Designing a Full Adder

1. Identify the inputs and outputs: The inputs for a full adder are A, B, and Cin (the carry in bit from a previous stage), and the outputs are Sum (the sum of A, B, and Cin) and Cout (the carry out bit).
2. Build the truth table: The truth table for a full adder will have 8 rows, representing all possible combinations of inputs and their corresponding outputs.
3. Write the boolean equations: Based on the truth table, you can write the boolean equation for the Sum output as Sum = A'B'Cin + A'BCin' + AB'Cin' + ABCin, and for the Cout output as Cout = AB + BCin + ACin + ABCin.
4. Design the gate-level circuit: The gate-level circuit for a full adder consists of two half adders and an OR gate.