Digital circuits come in several varieties, but one very basic and important type is the gate, which is used for controlling actions rather than just for counting. More than 100 years before digital electronics was established, an English mathematician called George Boole proved that all of the statements in human logic could be expressed by combinations of three rules which he called AND, OR, and NOT. This logic system is now known as Boolean logic. We will see later how these gates can also be used for simple arithmetic actions.

The importance of all this is that, if we can provide digital gate actions corresponding to these three rules of AND, OR, and NOT, we can construct a circuit that will give a 1 output for any set of logical rules. For example, if we want to have an electric motor switched on when a cover is down, a switch is up, and a timer has reached zero, or when an override switch is pressed, then this set of rules can be expressed in terms of AND, OR, and NOT, and a gate or set of gates can carry out the action.

Figure 10.1 shows the symbols that are used for the three main gate types, the AND, OR, and NOT gates, using two-input gates in the example. The action of these gates will be discussed in detail shortly, but for the moment note that the small circle shown in the NOT symbol is used to mean inversion, converting 1 to 0 or 0 to 1. We can combine the other basic symbols with the NOT circle symbol to give symbols for other gate actions. The early digital integrated circuits (ICs) would typically contain four gates of one type per chip, but modern electronic equipment is more likely to use custom-made chips, with all the gates and their connections formed in one process, using thousands or millions of gates on one chip.

Once again, this makes it more useful to show block diagrams rather than gate circuit details. A gate circuit diagram will consist of a large number of gate symbols with joining lines so that the output of a gate will be connected to one or more other gate inputs. Provided that we know what each basic type of gate does, we can analyze the action of complete gate circuits. In this book we are concerned more with block diagrams than with gate circuits, but some knowledge of gate circuits is useful, and in any case, these are closer in spirit to block diagrams than to circuit diagrams.

For example, if there are four inputs to a gate, then the number of possibilities is 2 ⁴= 16, and its truth table will consist of 16 lines. For a lot of truth tables, there is only one output that is different from the rest, and it is easier to remember which one this is than to try to remember the whole of a truth table.

Figure 10.2 shows truth tables for the basic two-input AND, OR, and NOT gates. Of these, the NOT gate is a simple one, with just one input and one output. Its action is that of a logic inverter. If the input is 0, then the output is not0, which is 1. If the input is 1, then the output is not1, which is 0. The other two gate types permit more than one input, and the examples show two inputs, the most common number. The action of the AND gate is to give a 1 output only when both inputs are at 1, and a 0 output for any other combination. The action of the OR gate is to give a 0 output when each input is 0, but a 1 for any other combination of inputs. The same arguments apply to gates with more than two inputs.

The need to use codes for digital information often leads to problems in transmitting the digital signals, because we very often cannot provide a signal line for each code signal. Suppose, for example, that we have a set of eight switches, any one of which can be ON (1) or OFF (0), but not allowing more than one switch to be ON at a time. Suppose also that we need to pass this information to some unit which might be a controller or some type of recorder. One obvious method is to use eight lines, one for each switch. A less obvious method is to use the binary numbers for 0 to 7 (a total of eight codes), which cover the range 000 to 111, using only three lines. A circuit that carries out this change from using eight lines to using three lines is called an 8 to 3 encoder. Encoders are used to reduce the number of signal channels needed for data.

Figure 10.15 shows an encoder block and truth table for the example of eight to three transformation. A decoder for three lines to eight, also shown here, would work in the opposite way, with a 3-bit binary input and a set of eight lines out, only one of which could be at level 1 for each combination of input bits. You might, for example, use the outputs from the decoder to operate warning lights, if only one at a time needed to be illuminated.

An encoder is needed when each of a set of inputs must generate a unique code pattern. For example, imagine a set of 16 keys (a hexadecimal keypad) for which each of the 16 input key characters must generate a unique 4-bit output code; we assume that only one key is pressed at a time. This encoder would require 16 inputs, only one of which is selected at any one time, and would provide four output lines to provide the parallel bit pattern. If we needed to reconstitute the pattern of lines at the input, we would use a decoder that would have four input lines and would use the bits on these lines to select one and only one of 16 output characters.

Encoders and decoders can be made using gates, and Figure 10.16 shows an example of a 2 to 4 line decoder using inverters and AND gates, along with a truth-table analysis of the action.

Now let’s look at a multiplexer. Figure 10.17 shows in block form what a 4 to 1 multiplexer is expected to do. There are four data inputs, two address inputs, and a strobe input. The address inputs are used to select one of the four data lines, using an encoding action (which is why encoders and multiplexers are often taken to be almost identical). The data on the selected line is transferred to the single output line when the signal on the strobe line is low (logic 0). This allows all of the data to be sent down one line, a bit at a time, by establishing an address number, pulsing the strobe input, and repeating this for another address number until you have cycled through all the address numbers.

Figure 10.18 shows a gate circuit that can carry out the action of multiplexing a set of four inputs. For four inputs, a 2-bit address number is needed to select which input will be connected to the output line when the strobe input goes to logic 0. The opposite action of a demultiplexer is shown in block form in Figure 10.19. There is a single data input and a strobe input, along with the address inputs, in this case using two lines for the addresses of four output lines. Once again, the data on the input line will appear at the selected output line when the strobe pulse voltage is low, and the truth table is in Figure 10.19 with the selected output data line in this example taking the logic value of 0 (the same as the data line input) when the strobe appears (assuming that strobing occurs when the strobe input is low).