Introduction
Having a basic understanding of how a computer works is essential to successfull programming. Merely jumping in blindly and trying to hack some code together is not even a remotely good practice. Lacking the basic knowledge leads to bugged and bloated programs, not to mention long hours of coding, testing and debugging. Wouldn't it be nice if everyone took the time to properly write a fast and efficient program, instead of rushing it out the door??
This lesson teaches the very basics of computers, binary numbers and boolean logic. These are simple concepts, and if you do not already understand them, you should learn them.
For a much more in-depth
(and better) discussion, go to:
Binary Numbers: Art
of Assembly - Chapter 1
Boolean Logic : Art
of Assembly - Chapter 2
Binary
Numbers
Decimal Numbers:
In order to understand binary numbers, we must first refresh our knowledge of the decimal number system. If you do not already know this information, assembly programming is probably not for you....instead, go and play some video games, they're very entertaining. Anyways...
The decimal number system is base-10, meaning its digits are based upon powers of 10. It also means that each digit can represent one of 10 different values (0-9). For example, the number 443556 can be represented as:
443556 = 4x105 + 4x104 + 3x103 + 5x102 + 5x101 + 6x100
= 400,000 + 40,000 + 3,000 + 500 + 50 + 6
Binary
Numbers:
The binary number system
is base-2; its digits are based upon powers of 2. Each digit can
represent one of 2 different values (0,1).
To convert binary to decimal
is simple:
0100 10102 = 0x27 + 1x26 + 0x25 + 0x24 + 1x23 + 0x22 + 1x21 + 0x20
= 64 + 8 + 2 = 7410
Converting decimal to
binary is slightly more complex: You'll need to work backwards, finding
the greatest power of 2 which is less than the number you wish to convert.
Then continue for each lesserpower of 2 until 20. For
Example, convert 1998 to binary:
1x210 = 1024
1998-1024 = 974
1x29 = 512
974-512 = 462
1x28 = 256
462-256 = 206
1x27 = 128
206-128 = 78
1x26 = 64
78-64 = 14
...
1x23 = 8
14-8 = 6
1x22 = 4
6-4 = 2
1x21 = 2
2-2 = 0
199810 = 0111 1100 11102
In a computer, all data is stored in binary form. Each binary digit in a computers is known as a bit. A byte is equal to 8 bits, while a word is 16 bits, and a dword is 32 bits.
Hexadecimal Numbers:
Hexadecimal (Hex) numbers are base-16. They are a concise way of representing binary numbers. It represents each byte of data as a base-16 number. Because there are only 10 numerals, the letters A-F are used for the remaining 6 digits. Following is a table of binary numbers and their hexadecimal equivalents:
Bin Hex
Bin Hex Bin Hex
Bin Hex
0000 0
0100 4 1000 8
1100 C
0001 1
0101 5 1001 9
1101 D
0010 2
0110 6 1010 A
1110 E
0011 3
0111 7 1011 B
1111 F
Therefore: 0010 1001 10102 = 29A16
As you can see, 29A is much
easier to read and write than it is in binary form. Plus, the conversion
is trivial, so it makes sense to use hex numbers when dealing with computers...
Boolean
Logic
Everyone should remeber logic from math class.. If not heres a brief introduction to it. Boolean logic is a math system closed over the values 0 and 1. I will not give a complete discussion of boolean logic, justa few minor points that may be useful for programming.
AND
OR
XOR NOT
X Y Z
X Y Z X Y
Z X Z
0 0 0
0 0 0 0 0
0 0 1
0 1 0
0 1 1 0 1
1 1 0
1 0 0
1 0 1 1 0
1
1 1 1
1 1 1 1 1
0
For a plaintext copy:
a_tut1.txt