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. Include detailed steps.

Answer 1

To design a half adder, you start with its truth table and derive the sum as A XOR B and the carry as A AND B. For a full adder, you extend the truth table to include a carry-in and derive the sum as A XOR B XOR Cin, and the carry-out as (A AND B) OR (B AND Cin) OR (A AND Cin). Then, you draw their schematic gate-level circuits accordingly.

Step-by-step explanation:

Designing a Half Adder and Full Adder

To design a half adder and a full adder, we must start by understanding their functions. A half adder is used to add two single binary digits, and it provides two outputs: the sum (S) and the carry (C). The full adder, on the other hand, adds three binary digits including a carry from the previous addition, also providing sum and carry outputs.

Half Adder Design

Here is the truth table for a half adder:

From this table, we get the boolean equations for the sum and carry:

The schematic gate-level circuit will include an XOR gate for the sum and an AND gate for the carry.

Full Adder Design

The truth table for a full adder is:

And the boolean equations are:

The full adder gate-level circuit will involve two XOR gates, two AND gates, and one OR gate to combine the carry outputs.