One of the earliest forms of solid-state digital logic came into use at the end of the 1950's. It was based on the use of diodes. Although it doesn't work very well (and has now virtually vanished) its a useful starting point to see how binary electronics can be made to work. Figure 11.1 shows the circuit of an ‘OR’ gate built using a pair of diodes and a resistor. It also shows the standard symbol used to represent an ‘OR’ gate on diagrams of digital logic. (The same symbol's are used no matter how the gates are made. From the abstract logical point of view the details of the electronics are irrelevant.)
Digital electronics uses “high” and “low” voltages to represent the ones and zeros of binary numbers. One of the advantages of digital systems is that the precise voltages used aren't very important. For many kinds of circuits “high” (= “1”) is usually anything in the range from just above +2·5V to +5V, and “low”(= “0”) is anything in the range 0V to about +2·5V. Ideally, therefore, we'd expect a logical one to be signalled by about 5V and a zero by about 0V.
The gate shown in figure 11.1 has two inputs, A & B , and an output, C. We can represent the signals at these inputs & outputs in two ways. We can specify the actual voltages, Va , Vb, and Vout at these places, or we can say that the logic levels, A, B, C, in these places are “1” (“high”) or “0” (“low”) depending upon whether the appropriate voltages are greater or less than 2·5V. We can then draw up a truth table (a list of what output various input possibilities produce) for the circuit/gate. For this gate the truth table is as shown below.
When both inputs are presented with logical zeros we can expect that Va = Vb = 0 Volts. Since the output ends of the two diodes are connected to ground (0V) through a resistor and nothing in the circuit is providing any volts, the output will also be Vout = 0 Volts - i.e. when the two inputs are zero, the output will be zero.
When we apply +5V to one of the inputs (equivalent to a logical “1”) the diode connected to it will be forward biassed. It therefore passes current from the input signal through the resistor, R. From a previous section on diodes we know that about half a volt will be ‘dropped’ across a diode when it is conducting. Hence an input of +5V will produce an output voltage at the top of the resistor of about +4·5V. Since this is greater than 2·5V it means that a logical “1” on either input will produce a “1” at the output. Hence if either A OR B = 1 then C = 1. Note that if both A and B are “1” then the output, C is also “1”. The action of the OR gate is said to be inclusive. When we use the logical circuit symbol shown in figure 11.1 or use the logical expression
we're saying, ‘If either A or B or both are “1” then C is “1” ’.
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University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.