Final answer:
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
- 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).
- 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.
- 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.
- 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
- 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).
- 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.
- 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.
- Design the gate-level circuit: The gate-level circuit for a full adder consists of two half adders and an OR gate.