Bits And Bytes - AMSTRAD CPC464 User Manual

If the ultimate answer is either 0 or 1, then there is no possibility of it being ' nearly' correct. The fact
that computers can sometimes appear to make errors when handling numeric data is due to the
limitation of the size of numbers it can process requiring ' oversize' data to be squeezed down to fit
the space available, or truncated, leading to rounding errors. eg 999,999,999 becomes 1,000,000,000.
In a world where the only two numbers available are 0 or 1, how do you then count beyond 1 ?

Bits and Bytes

We just happen to be used to understanding numbers based on the decimal system where the
reference point is the number 10 - ie there are ten digits available to represent quantities in range
from 0 to 9 (which is used in preference to the expression 1 to 10). The system where numbers range
from 0 to 1 is the binary system, and the units in which the system operates are called bits - an
abbreviated form of ' Binary digiT' . It might be less confusing if you forget all about the decimal
context of the 0 and the 1, and use two totally different symbols to represent their function: fl and *
can be used equally well, as long as there is consistency throughout.
The relationship between bits and decimal notation is simple to understand:
It' s actually conventional to declare the maximum number of binary digits being used by adding
leading zeros to make up the number to the full number of bits:
decimal 7 becomes
00111 binary
using 5 bit notation
In the binary system, the figures may be considered merely as indicators in columns to specify
whether or not a given power 2 is present (l), or not (0).
2 = 1
0
2 = 2 = 2 = 2(2 )
l 0
2 = 4 = 2x2 = 2(2 )
2 1
2 = 8 = 2x2x2 = 2(2
3 2
2 = 16 = 2x2x2x2 = 2(2
4
so the columns look like:
2 2
4 3
1 0
(16 0
In order to provide a shorthand method of referring to binary digit information, the term byte is used
to denote 8 bits of information. The highest number that can be stored in a byte is then (binary)
11111111 - or (decimal) 255. This implies 256 actual variations, including 00000000, which is still
perfectly valid data to a computer.
Computers tend to manipulate data in 8 bit multiples. 256 is not a very large number, so in order to
acheieve an acceptable means of handling the memory, two bytes are used to provide a method of
addressing memory which is in the form of an array, with a horizontal and vertical address by which
the elements of that array can be located:
)
)
3
2
2
0
0
2 2
l 0
1 1
2 1) = 19