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1

Binary numbers

## 1.1 Numbers within a computing machine

Our study of computing machines begins by looking at the basic components from which a machine might be constructed. We begin by asking how numbers may be represented in a machine.

The simplest numbers that we want to represent in the machine are the unsigned integers. These are whole numbers without a sign, for example, 0, 1, 2, 3, … The mechanical calculators of yesteryear and the car mileage meter of today both store unsigned integers on what are effectively cogs having ten numbered teeth1. Thus a simple two-digit calculator capable of addition and subtraction will comprise two cogs, one indicating units, the other indicating tens, Figure 1.1.

Figure 1.1 Two cogs representing the ...

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