If you are using hex notation & you want to make the fact quite plain, then write 'h' at the end of the
number, & say 'hex'. For instance, for a hundred & fifty eight, write '9Eh' & say 'nine E hex'.
You will be wondering what all this has to do with computers. In fact, computers behave as though they
had only two digits, represented by a low voltage, or off (0), & a high voltage, or on (1). This is called the
binary system, & the two binary digits are called bits: so a bit is either 0 or
1.
In the various systems, counting starts off
The important point is that sixteen is equal to two raised to the fourth power, & this makes converting
between hex & binary very easy.
To convert hex to binary, change each hex digit into four bits, using the table above.
To convert binary to hex, divide the binary number into groups of four bits, starting on the right, & then
change each group into the corresponding hex digit.
For this reason, although strictly speaking computers use a pure binary system, humans often write the
numbers stored inside a computer using hex notation.
The bits inside the computer are mostly grouped into sets of eight, or bytes. A single byte can represent
any number from nought to two hundred & fifty five (11111111 binary or FF hex), or alternatively any
character in the ZX81 character set. Its value can be written with two hex digits.
Two bytes can be grouped together to make what is technically called a word
. A word can be written
using sixteen bits of hex digits, & represents a number from 0 to (in decimal) 2
16
-1 = 65535.
A byte is always eight bits, but words vary from computer to computer.
Summary
Decimal, hexadecimal & binary systems.
Bits & bytes (don't confuse them) & words.
Exercises
1. The Martian unit of currency is the pound, & it is divided into sixteen ounces. How would you convert
A1 a hundred & sixty one
: :
: :
FE two hundred & fifty four
FF two hundred & fifty five
100 two hundred & fifty six
English Decimal Hexadecimal Binary
nought 0 0 0 or 0000
one 1 1 1 or 0001
two 2 2 10 or 0010
three 3 3 11 or 0011
four 4 4 100 or 0100
five 5 5 101 or 0101
six 6 6 110 or 0110
seven 7 7 111 or 0111
eight 8 8 1000
nine 9 9 1001
ten 10 A 1010
eleven 11 B 1011
twelve 12 C 1100
thirteen 13 D 1101
fourteen 14 E 1110
fiveteen 15 F 1111
sixteen 16 10 10000
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