Sinclair ZX81 - Chapter 24 - Counting on your fingers

Chapter 24 - Counting on your fingers
The next chapter digs inside the computer a bit, but before we look at that it would be as well to describe
how computers count: they do it using the binary
system, which means that they have no fingers - they are
all thumbs.
Most European languages count using a more or less regular pattern of tens - in English, for example,
although it starts off a bit erratically, it soon settles down into regular groups:
twenty, twenty one, twenty two,...,twenty nine
thirty, thirty one, thirty two,...,thirty nine
forty, forty one, forty two, ...,forty nine
& so on, & this is made even more systematic with the Arabic numerals that we use. However, the only
reason for using ten is that we happen to have ten fingers & thumbs.
Now suppose Martians have three extra fingers on each hand (in so far as one can call them fingers): so
instead of using our decimal system, with ten as its base, they use a hexadecimal (or hex, for short)
system, based on sixteen. They need six extra hex digits in addition to the ten that we use, & they happen
to write them as A, B, C, D, E & F. And what comes after F? Just as we, with ten fingers, write 10 for ten,
so they, with sixteen, write 10 for sixteen. Their number system starts off:
j
ust as ours does, but then it carries on
Hex English
0 nought
1 one
2 two
: :
: :
9 nine
A ten
B eleven
C twelve
D thirteen
E fourteen
F fifteen
10 sixteen
11 seventeen
: :
: :
19 twenty five
1A twenty six
1B twenty seven
: :
: :
1F thirty one
20 thirty two
21 thirty three
: :
: :
9E a hundred & fifty eight
9F a hundred & fifty nine
A0 a hundred & sixty