# Number System Conversion - Decimal to Binary, Octal and Hexadecimal

## Why do we need number system conversions?

Computer is an electronic or digital device that operates based on an on /off switch.

1 represents ON, and 0 represents OFF.

The two digits 0 and 1 are called binary numbers.

Computer can understand only the two binary numbers (0s and 1s).

• As humans, we use the decimal number system in our day to day life.
• For computers, every decimal number and instruction has to be converted into a binary number.
• For large decimal number, the binary representation is too long that is very difficult for the user to interpret.
• To simplify usage and interpretation, the octal and hexadecimal numbering systems are used.

A group of four bits of the binary number is equal to one digit of a hexadecimal number

A group of three bits of the binary number is equal to one digit of the octal number.

Long numbers are less lengthy in hexadecimal system. Hence, Hexadecimal numbers are used more than the octal numbers. Octal is still utilized in a few scenarios.

For easy reading and understanding, the programmer can often use a hexadecimal numbering system. Nowadays, most computers are designed to process the hexadecimal numbers.

4 numbering systems available for our use on which each one can be converted to other three number systems. The possible number system conversions are

Following table shows the Decimal, Binary, Octal, and Hexadecimal equivalents:

DecimalBinaryOctalHexa Decimal
Base 10Base 2Base 8Base 16
0 000
1 111
2 1022
3 1133
4 10044
5 10155
DecimalBinaryOctalHexa Decimal
6 11066
7 11177
81000108
91001119
10101012A
DecimalBinaryOctalHexa Decimal
11101113B
12110014C
13110115D
14111016E
15111117F
DecimalBinaryOctalHexa Decimal
161 00002010
171 00012111
181 00102212
191 00112313
201 01002414
DecimalBinaryOctalHexa Decimal
211 01012515
221 01102616
231 01112717
241 10003018
251 10013119
261 1010321A
DecimalBinaryOctalHexa Decimal

# Number System Conversion - Decimal to Binary, Octal and Hexadecimal

## Why do we need number system conversions?

Computer is an electronic or digital device that operates based on an on /off switch.

1 represents ON, and 0 represents OFF.

The two digits 0 and 1 are called binary numbers.

Computer can understand only the two binary numbers (0s and 1s).

• As humans, we use the decimal number system in our day to day life.
• For computers, every decimal number and instruction has to be converted into a binary number.
• For large decimal number, the binary representation is too long that is very difficult for the user to interpret.
• To simplify usage and interpretation, the octal and hexadecimal numbering systems are used.

A group of four bits of the binary number is equal to one digit of a hexadecimal number

A group of three bits of the binary number is equal to one digit of the octal number.

Long numbers are less lengthy in hexadecimal system. Hence, Hexadecimal numbers are used more than the octal numbers. Octal is still utilized in a few scenarios.

For easy reading and understanding, the programmer can often use a hexadecimal numbering system. Nowadays, most computers are designed to process the hexadecimal numbers.

4 numbering systems available for our use on which each one can be converted to other three number systems. The possible number system conversions are

Following table shows the Decimal, Binary, Octal, and Hexadecimal equivalents:

DecimalBinaryOctalHexa Decimal
Base 10Base 2Base 8Base 16
0 000
1 111
2 1022
3 1133
4 10044
5 10155
DecimalBinaryOctalHexa Decimal
6 11066
7 11177
81000108
91001119
10101012A
DecimalBinaryOctalHexa Decimal
11101113B
12110014C
13110115D
14111016E
15111117F
DecimalBinaryOctalHexa Decimal
161 00002010
171 00012111
181 00102212
191 00112313
201 01002414
DecimalBinaryOctalHexa Decimal
211 01012515
221 01102616
231 01112717
241 10003018
251 10013119
261 1010321A
DecimalBinaryOctalHexa Decimal