Computer Data Processing System

Number system is a way to represent the magnitude of a physical item. Number system uses a base number or base (base / radix) that tertenntu.

Understanding numbers:
Numbers are the physical representation of the observed data. Numbers can be represented in various forms, which are then classified in a number system, but have the same meaning.

To demonstrate a type number, typically a number that will be represented in a number of conversion followed behind with a code that describes the type of number, shape

like this is called a radix or base.

1. Decimal number system (decimal), Decimal numbers are encoded with 10 or d,
2. The binary number system (binary), Binary number encoded with 2 or b,
3. Octal number system (octal) .bilangan Octal encoded with 8 or o,
4. Hexadecimal numbering system (hexadecimal), hex encoded with 16 or h.

example:
- Decimal Numbers 23 is usually written in 2310 or 23d, together with;

- Octal Numbers 27, which is usually written 278 or 27o, together with;

- Hex Numbers 17, which is usually written in 1716 or 17h, together with;

- Binary Numbers are usually written 10111 101112 or 10111b,

1. Decimal Number
Decimal number is a number that uses base or base 10, in the sense of having 10 different digits that have a value of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
We can produce again another number in the system, which we refer to as the number of tens or often written 10s, hundreds (100's), and continue.

Decimal number system commonly known as a base 10 number system, because each decimal number using base (radix) 10, as shown in the following example:
decimal number 123 = 1 * 102 + 2 * 101 + 3 * 100

The following table displays the decimal number system (base 10), binary number system (base 2) number system / octal numbers (base 8), and hexadecimal number system (base 16) which is the basis of knowledge to learn the digital computer. Octal number is formed from its binary number by grouping every 3 bits of the far right (LSB). While the hexadecimal number can also be formed easily from its binary numbers by grouping each 4 bits from the right end.

Decimal Binary (8 bits) Octal Hexadecimal
0 0000 0000 000 00
1 0000 0001 001 01
2 0000 0010 002 02
3 0000 0011 003 03
4 0000 0100 004 04
5 0000 0101 005 05
6 0000 0110 006 06
7 0000 0111 007 07
8 0000 1000 010 08
9 0000 1001 011 09
10 0000 1010 012 0A
11 0000 1011 013 0B
12 0000 1100 014 0C
13 0000 1101 015 0D
14 0000 1110 016 0E
15 0000 1111 017 0F
16 0001 0000 020 10


example 1
decimal value 5734 = 5000 + 700 + 30 + 4
= 5 x 1000 + 7 x 100 + 3 x 10 + 4x 1
= 5 x 103 + 7 x 102 + 3 x 101 + 4 x 100
contoh2
52 710 (decimal), can also be expressed:
527 = 5 x 102 + 2 x 101 + 7 x 100
= 5 groups of hundreds (10x10) + 2 groups of tens
+ 7 units

Binary 2.Bilangan

Since the first electronic computer is used, has been operating with the use of binary numbers, ie numbers with base 2 numbers in the system. All program code and data are stored and manipulated on a computer in a binary format that is machine code komputer.Sehingga all calculations were processed using binary arithmetic, the number that has only two possible values​​, namely 0 and 1 and is often referred to as bits (binary digits) or in the electronic architecture commonly referred to as the digital logic.

Octal 3.Bilangan

Octal number system is based on eight (8) and has eight symbols, namely 0, 1, 2, 3, 4, 5, 6, 7 In general, the number system is used for playing music notation at the time, so it is often called the octave.

Decimal number is expressed as a binary number will be shaped as follows:
Decimal Binary (8 bits)
0 0000 0000
1 0000 0001
2 0000 0010
3 0000 0011
4 0000 0100
5 0000 0101
6 0000 0110
7 0000 0111
8 0000 1000
9 0000 1001
10 0000 1010
dst

example: convert decimal number into binary
decimal = 10.
approach based on the above reference number 10 is 8 (23), then the result of the reduction of 10-8 = 2 (21). so it can be described as follows
10 = (1 x 23) + (0 x 22) + (1 x 21) + (0 x 20).
from the above calculation of the binary number 10 is 1010

4.Bilangan Hexadecimal

Hexadecimal numbers are often called hex-based 16 has a value that is symbolized by 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F. The presence of hex numbers surgery due to the computing operations on binary numbers for large data would be hard to read, so the number heksadsimal often used to describe computer memory or instruction. Each hexadecimal digit represents four binary bits (nible), and 2-digit hexadecimal number represents one byte.

For example, the hex number 41 (2 nible) in ASCII format representing the character "A", the hex number 42 represents the character "B", and so on.
Decimal value that is equivalent to each of the symbols shown in the following table:
0hex = 0dec = 0oct 0 0 0 0
1hex = 1dec = 1oct 0 0 0 1
2hex = 2dec = 2oct 0 0 1 0
3hex = 3dec = 3oct 0 0 1 1

4hex = 4dec = 4oct 0 1 0 0
5hex = 5dec = 5oct 0 1 0 1
6hex = 6dec = 6oct 0 1 1 0
7hex = 7dec = 7oct 0 1 1 1

8hex = 8dec = 10oct 1 0 0 0
9hex = 9dec = 11oct 1 0 0 1
Ahex = 10dec = 12oct 1 0 1 0

fractions
Fractions (fractions) is the location or position numbers are after the decimal (point-to-decimal). Value of different fractions with integer values ​​in decimal. Need diingan, that fraction in Indonesia format is a comma (comma), while the UK or fractional format using point (point) (compare with Indonesia, that point is usually used to limit the value of thousands). In this discussion, the comma will be used to designate any fractional value, in accordance with the format Indonesia.

Integer representation / Integer

1 Not Signed Integer can be represented by:
- Binary numbers
- octal
-heksadesimal
-graycode
- BCD (binary coded decimal)
-Hamming code

2 Integer marked (positive or negative) can be represented by:
- Sign / Magnitude (S / M) (marked with numbers / magnitut)
- 1's complement (complement 1)
- 2's complement (complement of 2)
positive integers, there is no difference in the three kinds of representations of numbers above.

Sign / Magnitude

Negative representation of a number is obtained by changing the shape of the positive bits on the MSB be worth 1.
If N bits used for data representation, the range of values ​​that can be represented is -1 -2 N-1 s / d 2 N-1-1
Example: if the 5 bits used for the representation of numbers, then: +3 -3 = 00011 = 10011

complement 1
Negative representation of a number is obtained by engkomplemenkan whole bits of positive value. If N bits used for data representation, the range of values ​​that can be represented is N-1 -1 -2 to 2 N-1 -1
example:
If used 5 bits for the representation of numbers -3 +3 = 00011 = 11100
From the above example can be seen in the form of presentation that MSB is used to designate the sign of the number.
The way this is called the "sign / magnitude". If the MSB = 0, then the positive (+) and if MSB = 1, then the negative (-)

sumber: http://badaklucu.blogspot.com/2010/02/sistem-pengolahan-data-komputer.html