AMSTRAD CPC464 User Manual page 224

This array can locate up to (10x10) items of information using address numbers that lie in the range
1 to 9. The item stored at position 3,5 is a ' 1' - as is the item at 5,5.
So a binary array of 256x256 can handle 65,536 individual locations using 8 bit addresses for the
vertical and horizontal axes of the array. So our ' 0' and ' 1' have progressed to being capable of
identifying one of 65,536 unique elements.
The next level of shorthand for binary is the kilobyte &Byte or simply ' K' ) which is 1024 bytes. 1024
is the nearest binary multiple to the more familiar decimal use of the term ' kilo' - and explains why a
computer described as having a ' 64K' memory does in fact have a memory of 65,536 bytes (64 x
1024).
Thankfully, the BASIC interpreter does all the necessary conversions for you, and it is quite possible
to become a proficient programmer without a complete understanding of binary. Although an
appreciation of the significance of binary will help you spot the many ' magic' or significant numbers
that inevitably crop up as you work through the science of computing.
It' s worth spending some effort to acquire an understanding of binary and the various significant
numbers 255, 1024 etc., since it is very unlikely that these will change from the being the bedrock of
computer operation in the forseeable future. The certainty and simplicity that comes from working in
only two states will prevail over the enormously increased complexity that would result from any
other number base.
However....
Simple and elegant as it is, binary notation is longwinded and prone to inaccuracy as it cannot be
easily read at a glance. Binary has a number of associated counting systems that act as shorthand
for programmers. One such number system is widely used in microcomputing called Hex (an
abbreviation of hexadecimal).
0 1 2 3 4 5
1
2
3
4
5 1 1
6
7
8
9
6 7 8 9