Computer number format:
A computer number format is the internal representation of numeric values in digital computer and calculator hardware and software. Normally, numeric values are stored as groupings of bits, named for the number of bits that compose them. Different types of processors may have different internal representations of numerical values.
Requirement of Binary Number System:
Binary language is basically just two digits either 0 or 1. Each of these digits actually represent 'state'; let's call it 'On' and 'Off'. To understand this better in electronics; an 'on' state could be thought if as a positive voltage say 5V and 0 would represent 0V.
In this way, any number we give to the computer, it doesn't understand that number. It simply converts that number into the binary code. So that, the binary number is most required for any computer.
Binary Number Format:
Computer represent data in sets of binary digits. The representation is composed of bits, which in turn are grouped into larger sets such as bytes. A bit is a binary digit that represents one of two states. The concept of a bit can be understood as a value of either 1 or 0.
There are several types of formats
Number System |
Base |
Used Digits |
| Binary | 2 | 0,1 |
| Octal | 8 | 0,1,2,3,4,5,6,7 |
| Decimal | 10 | 0,1,2,3,4,5,6,7,8,9 |
| Hexadecimal | 16 | 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F |
Decimal to binary conversion:
For example, if we consider a number 25 then the conversion would be
the binary number for 25 is 11001.
- Binary to decimal conversion:
11001 = 1*2^4 + 1*2^3 + 0*2^2 + 0*2^1 + 1*2^0
= 16+8+0+0+1
= 25
Decimal to octal conversion:
For example, if we consider a number 137 then the conversion would be
The octal number for 137 is 211.
- Octal to decimal conversion:
211 = 2*8^2 + 1*8^1 + 1*8^0
= 128+8+1
= 137
Decimal to Hexadecimal conversion:
For example, if we consider a number 223 then the conversion would be
The hexadecimal number for 223 is 1315 or simply we can write DF.
- Hexadecimal to decimal conversion:
For example,
DF=13 15
13 15 = 13*16^1 + 15*16^0
= 208+15
= 223