Introduction to Digital Systems: Modeling, Synthesis, and Simulation Using VHDL

3.12 DESIGN EXAMPLES

3.12.1 Multiplexer

A multiplexer is a combinatorial circuit that has a number (usually, a power of 2) of data inputs (2ⁿ) and n select inputs used as a binary number to select one of the data inputs. The multiplexer has a single output, which has the same value as the data input selected. Now let us consider a 2 : 1 multiplexer. As the name indicates, it has two data inputs, x₁ and x₂, a select input, s, and a single output, y. The output of the circuit will be same as the value of input x₁ if s = 0; otherwise the output will be equal to x₂. We can construct a truth table based on these requirements. The truth table of a 2: 1 multiplexer is shown in Figure 3.11.

From the truth table we can derive the logical expression for the output y:

After simplification, the expression is reduced to

Figure 3.11 Truth Table of a 2:1 Multiplexer

Figure 3.12 Logic Diagram of a 2:1 Multiplexer

which can be realized using one OR gate and two AND gates. The logic diagram for a 2:1 multiplexer is shown in Figure 3.12.

3.12.2 Half-Adder

The half-adder is an example of a simple ...