Binary Number
The binary number is a value system and a special code for computers, which contains only the two numbers 0 (power off) and 1 (power on). A binary number also values of the basis 2.
The construction of the decimal number 2 needs two positions, because 0 and 1 are for the decimal numbers 0 and 1, also must be the decimal number 2 in binary numbers "01". Every new position is another power of 2 (2, 4, 8, 16, 32, ...). With n binary numbers can be constructed 2 to the power of n eventualities.
This table views the construction of the first 16 values of the decimal system (0 until 16) with the first 4 positions with the binary numbers.
Binäre Zahl | Dezimalzahl |
---|---|
0 | 0 |
1 | 1 |
10 | 2 |
11 | 3 |
100 | 4 |
101 | 5 |
110 | 6 |
111 | 7 |
1000 | 8 |
1001 | 9 |
1010 | 10 |
1011 | 11 |
1100 | 12 |
1101 | 13 |
1110 | 14 |
1111 | 15 |
now 5 positions | |
10000 | 16 |
10001 | 17 |
etc. | etc. |
Exchanges[edit]
Very important is for the programmer the exchange form binary numbers in decimal numbers or the reverse.
- Binary numbers into decimal numbers:
For example this binary number 1011 That must be insert in this formula:
PRINT "DECIMAL NUMBER: " 1*2↑3 + 0*2↑2 + 1*2↑1 + 1*2↑0
Screenoutput: DECIMAL NUMBER: 11
- Decimal numbers into binary numbers: 11
The converting of a decimal number into a binary number is a little bit difficult. The easiest way is the method of devision. A decimal number will be devided so long through 2 until the rest is 0. At each step will be noted the rest. For each rest is noted a 1, too. When the 1 is be added backwards (down to up), you get the correct binary number.
11 : 2 = 5 rest ...1 05 : 2 = 2 rest ..1 02 : 2 = 1 rest .0 01 : 2 = 0 rest 1 ---------------------- Binary Number: 1011
In computer science didn't exist only the binary system and decimal system, also hexadecimal and many more like a nibble1011 (4 bits).
Links[edit]
Wikipedia: Binary_numeral_system |