Understand hex numbers

understand ....

hex numbers

This file is intended for those interested in 32 bit assembler programming, in particular for Windows.

Programmers represent numbers in hex for a number of reasons. One reason is because this is a convenient way to visualise the number in data. This not only helps when dealing with large numbers, but it also enables the programmer to know what bits in data are "set" or "clear" in a particular number, something useful when testing individual bits. Another reason is that using hex numbers makes it easier and less error prone to use the logical instructions (eg. OR, AND, TEST, BT).
Hex numbers are to base sixteen. Hex is short for "hexadecimal" which comes from "hex" meaning six and "dec" meaning ten. Each hex number has a value of 0 to 9 or A, B, C, D, E, or F. Each hex number represents four bits of binary data. Here are the values which can be created from four bits and the hex and decimal values in each case:-

binary
0000
0001
0010
0011
0100
0101
0110
0111
1000
1001
1010
1011
1100
1101
1110
1111

hex
0
1
2
3
4
5
6
7
8
9
A
B
C
D
E
F

decimal
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

A byte can be represented as two hex numbers, a word as four hex numbers and a dword as eight hex numbers. You can see the real advantage of hex numbers when looking at larger numbers which become unwieldy when represented in decimal:-

binary
10000000
1000000000000001
1111111111111111
10000000000000000000000000000001
11111111111111111111111111111111

hex
80
8001
FFFF
80000001
FFFFFFFF

decimal
128
32,769
65,535
2,147,483,649
4,294,967,295

(byte)
(word)
(word)
(dword)
(dword)