# Combinational Logic Circuit Design Combinational logic circuits are systems where the output solely depends on the present input, without regard to previous inputs or states. These circuits are composed of basic logic gates: AND, OR, NOT, NAND, NOR, XOR, and XNOR. ## Design Steps Designing a combinational logic circuit involves the following steps: 1. **Problem definition**: Define the problem statement clearly. 2. **Truth Table creation**: Create a truth table based on the problem definition. 3. **Obtain simplified Boolean function**: Use methods like Karnaugh map (K-map) or Quine-McCluskey to simplify the Boolean function. 4. **Design the logic circuit**: Draw the logic diagram using the basic logic gates. ## Design Example: Half-Adder Let's design a half-adder. A half-adder is a combinational circuit that performs the addition of two bits. It has two inputs, A and B, and two outputs, S (sum) and C (carry). 1. The truth table for the half adder is: | A | B | S | C | |---|---|---|---| | 0 | 0 | 0 | 0 | | 0 | 1 | 1 | 0 | | 1 | 0 | 1 | 0 | | 1 | 1 | 0 | 1 | 2. The simplified Boolean functions obtained from the truth table are: S = A XOR B, C = A AND B. 3. The logic circuit for the half-adder can be drawn using an XOR gate for the Sum and an AND gate for the Carry. This example illustrates the process of designing a simple combinational logic circuit. More complex designs can be achieved by combining these basic gates and following the design steps. ## Note on Hardware Description Languages (HDL) In practice, combinational logic circuits are often designed and simulated using hardware description languages like VHDL or Verilog. For the half-adder example, the Verilog code would be: ```verilog module half_adder (input A, B, output S, C); assign S = A ^ B; // XOR operation for sum assign C = A & B; // AND operation for carry endmodule ``` This code describes the same logic as our drawn circuit and can be used in a simulator to verify the behavior of the half-adder.