Assembly - 101 Bases & Conversion

This post is the first one in the series about x86 Assembly. Topics to cover:

• Bases & Conversion

The most you can carry out of a single-column addition of 2 numbers is 1

Base 8 (Octal)

Octal
1 = 80
10 = 81
100 = 82
1000 = 83

Base 8 – Base 10

76225 (base 8)
= 8⁰ * 5
+ 8¹ * 2
+ 8² * 2
+ 8³ * 6
+ 8⁴ * 7
= 31893 (base 10)

Base 16 (Hex)

Base 16 – Base 10

8DB3H (base 16)
= 16⁰ * 3
+ 16¹ * 11
+ 16² * 13
+ 16³ * 8
= 36275 (base 10)

Base 10 – Base 16 (余数法, next smallest number)

413 (base 10)
= 16² * 1
+ 16¹ * 9
+ 16⁰ * 13
= 19DH (base 16)

Base 2 (Binary)

In real world, counting tells how many are there;
In CS, counting is about naming them,

In binary, a column’s value is either present (1) or not present (0).

Hex as Shorthand for Binary

Decimal	Hex	Binary
0	0	0000
1	1	0001
2	2	0010
3	3	0011
4	4	0100
5	5	0101
6	6	0110
7	7	0111
8	8	1000
9	9	1001
10	A	1010
11	B	1011
12	C	1100
13	D	1101
14	E	1110
15	F	1111

Converting every 4 binary digits (right to left) into a single hex digit.

Decimal    218
Binary  1101 1010
Hex        D A