number and the letter E stands for ‘exponential’. Sometimes we might want to

use bigger numbers still, for instance if we were talking about the number of

hydrogen atoms in the known universe. This has been estimated as about

1.7×10^77. Equally 1.7×10−77, with a negative power, is a very small number and

this too is easily handled using scientific notation. We couldn’t begin to think of

these numbers with the Roman symbols.

### Zeros and ones

While base 10 is common currency in everyday life, some applications require

other bases. The binary system which uses base 2 lies behind the power of the

modern computer. The beauty of binary is that any number can be expressed

using only the symbols 0 and 1. The tradeoff for this economy is that the

number expressions can be very long.

`Powers of 2 Decimal`

20 1

21 2

22 4

23 8

24 16

25 32

26 64

27 128

28 256

29 512

210 1024

How can we express 394 in binary notation? This time we are dealing with

powers of 2 and after some working out we can give the full expression as,

394 = 1 ×256+ 1 ×128+ 0 ×64+ 0 ×32+ 0 ×16+ 1 ×8+ 0 ×4+ 1 ×2+ 0 ×

so that reading off the zeros and ones, 394 in binary is 110001010.

As binary expressions can be very long, other bases frequently arise in

computing. These are the octal system (base 8) and the hexadecimal system