### Arithmetic of Computers

#### from Tenscope Limited

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## Introduction

### Some Notes on the Text

Inevitably things change over time. In some respects the text of the original book shows its age and some details now look slightly out of place. In producing this web site I have generally opted to retain the original text. These notes are intended as pointers to a few areas where some additional comment may be appropriate.

First, units. Here and there, examples refer, for instance, to feet or to temperatures in Fahrenheit. Nowadays, most children are likely to be taught about metres and degrees Celsius and may not encounter feet or degrees Fahrenheit at school.

Second, the octal number system. Those going on to delve further into computing are now relatively unlikely to see octal in practical use but are very likely to encounter the hexadecimal system, base 16, with symbols 0 to 9, A, B, C, D, E and F. The principles are identical, hexadecimal just uses a different base and more symbols and one hexadecimal digit corresponds to 4 binary digits, not 3 - so two hexadecimal digits constitute one, 8 binary bit, byte - nowadays the most commonly encountered unit of computer data.

Hexadecimal / base 16 is, in fact, briefly introduced on the very last page, though under the, now archaic, name of sexadecimal and using symbols +, -, j, n, l and t to represent 10, 11, 12, 13, 14 and 15 rather than the, now conventional and probably less confusing, A, B, C, D, E and F.

Third, logarithms and the slide rule. Log tables and slide rules are now history - pocket calculators and computers have taken over. But for anyone engaged in mathematics, physics, engineering and many other subjects, the understanding of the concepts of powers, exponents and logarithms is still as relevant as ever.

Fourth, gender. Some of the text uses he / his rather than she / her. When the book was, originally written, that was probably the norm. Readers should mentally substitute whatever pronouns they feel appropriate as they read. They should certainly bear in mind that girls are quite as capable in this field as boys - indeed, the first computer programme was arguably written by a lady, Ada Lovelace.

Fifth, original spellings have been retained - e.g. "realize", rather than "realise".

I have, however, corrected a few typographical errors in the original text. Any errors that remain are either ones I failed to spot in the original or ones which I have inadvertently introduced. Please let me know about any you notice and I will endeavour to correct them (email : info@arithmeticofcomputers.co.uk).

David Nutting
Tenscope Limited