## 2.4 Common Logic Forms

Knowing a simple set of logic forms will support a designer when categorizing control problems. The following forms are provided to be used directly, or provide ideas when designing.

### 2.4.1 Complex Gate Forms

In total there are 16 different possible types of 2-input logic gates. The simplest are AND and OR, the other gates we will refer to as complex to differentiate. The three popular complex gates that have been discussed before are NAND, NOR and EOR. All of these can be reduced to simpler forms with only ANDs and ORs, as shown in Figure 2.12 Conversion of Complex Logic Functions.

Figure 2.12 Conversion of Complex Logic Functions

### 2.4.2 Multiplexers

Multiplexers allow multiple devices to be connected to a single device. These are very popular for telephone systems. A telephone switch is used to determine which telephone will be connected to a limited number of lines to other telephone switches. This allows telephone calls to be made to somebody far away without a dedicated wire to the other telephone. In older telephone switch boards, operators physically connected wires by plugging them in. In modern computerized telephone switches the same thing is done, but to digital voice signals.

In Figure 2.13 A Multiplexer a multiplexer is shown that will take one of four inputs bits D1, D2, D3 or D4 and make it the output X, depending upon the values of the address bits, A1 and A2.

Figure 2.13 A Multiplexer