Appendix D - Hexadecimal conversion

The hexadecimal is widely used in the field of computers, but decimal is easier for the human to understand. Hexadecimal is based on the number 16, just as in the same way that decimal is based on the number 10. There are not 16 single digit numbers, so we are forced to use the first 6 letters of the alphabet as well as the 10 numbers to represent a hexadecimal digit. The first few numbers run:

Decimal	Hexadecimal
0	0
1	1
2	2
3	3
...	...
8	8
9	9
10	A
11	B
12	C
13	D
14	E
15	F
16	10
17	11
18	12
19	13
...	...
24	18
25	19
26	1A

and so on. The easiest way of converting hexadecimal to decimal is to split up the digits into single units, and then add up. We prefix hexadecimal numbers with the sign ”&•, and we also abbreviate it to ”hex•.

In decimal, we can think of the number 157 as being 100 + 50 + 7. The same is true for hexadecimal. The hexadecimal number &B8 is &B0 + &08, so to convert a two digit hexadecimal number to a decimal number, you only need to know the first 16 digits.

Hex	Decimal	Hex	Decimal
00	0	00	0
01	1	10	16
02	2	20	32
03	3	30	48
04	4	40	64
05	5	50	80
06	6	60	96
07	7	70	112
08	8	80	128
09	9	90	144
0A	10	A0	160
0B	11	B0	176
0C	12	C0	192
0D	13	D0	208
0E	14	E0	224
0F	15	F0	240

So, in the above example, &B8 is &B0 + &08, which is 176 + 8, which is 184. Similarly, &EF is &E0 + &0F, which is 224 + 15, which is 239.

Signed conversion

Some of the effects require signed nibbles, or bytes. If this is the case, then the following conversion numbers are useful:

Nibbles		Bytes
Hex	Decimal	Hex	Decimal
00	0	00	0
01	1	10	16
02	2	20	32
03	3	30	48
04	4	40	64
05	5	50	80
06	6	60	96
07	7	70	112
08	-8	80	-128
09	-7	90	-112
0A	-6	A0	-96
0B	-5	B0	-80
0C	-4	C0	-64
0D	-3	D0	-48
0E	-2	E0	-32
0F	-1	F0	-16

So, if you had to convert &EA into signed decimal, it is &E0 + &0A, which is -32+10, or -22. The largest number you can have is &7F, or 127, the lowest is &80, or 128. Similarly, for a two signed nibbles, the value &2F would mean the two values •2•, and ”-1•.