Computers: The OR operator

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The OR operator

The second logical operator is OR. Using the party example from the previous sections,

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The electrical circuit shown in Figure 2.4 reproduces the effect of this table. In this circuit, the switches A and B are in parallel, and current X will flow if either A orB (or both) are closed.

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The NOT operator

The third logical operator is NOT. In the example we have used already, NOT A means Ann is not going (to the party)

and NOT B means Barbara is not going. So if Ann is going is true, then NOT A is false. The truth table representing this is:

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In electronics, a NOT gate consists of a special sort of switch which closes and so makes a circuit when no current is applied to it, and opens and so breaks the circuit when there is a current.

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Combining logical operators

We can combine these logical operators (and the circuits which represent them) in any number of ways. Staying with the party example, Colin may decide to go to the party if:

(A OR B) AND NOT (A AND B) = 1

This means he will go to the party if

A ORB= 1, i.e. if Ann or Barbara go, AND if NOT (A AND B) = 1, i.e. if they don't both go.

So he'll go with one or the other but not both.

The truth table for this can be built up in stages. The first stage is to construct intermediate values for A OR B and NOT (A AND B). The stage combines these two intermediate results using the AND operator.

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Arithmetic and logic

Most of the work done by a computer involves arithmetic calculations. The basic task in this arithmetic is the addition of the two binary numbers 0 and 1. If A and B can each take either of these two values, the resulting values of A + B will be as follows:

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The last column of this table, which shows the results of the addition, really consists of two columns: a two's column (i.e. 10 in binary) and a units column. So we could rewrite the table like this:

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Notice that the two's column is identical to the results column of the A AND B truth table on page 26. The units column is the same as the results column of the (A OR B) AND NOT (A AND B) table in the last section.

This means that we can use logical operators, and there­ fore logic gates, to produce these two columns, and there­ fore to carry out binary calculations.

clip_image009Logic circuits

Logic gates, shown as the simple electrical circuits on earlier pages in this chapter, therefore lie at the heart of all computing. As you have learned, these gates consist of switches connected up in various ways. In a microprocessor,

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each switch is a transistor, and a gate is therefore a simple circuit containing two or more transistors.

Rather than draw these circuits each time we wish to show an AND, OR, or NOT gate, it is much easier to use symbols. These are shown in Figure 2.5. Figure 2.6 shows a circuit called a 'half-adder gate' which produces the (A OR B) AND NOT (A AND B) column of the above truth table.

(If you study this circuit, you will see that it does indeed represent this combination of logical operators.) As you learned in the last section, it is this combination of gates that carries out the basic task of addition.

There are other kinds of circuits used in the arithmetic logic units of computers, but they are all based upon the logical operators described in the previous sections, and consist of various combinations of the AND, OR, and NOT gates.

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