Number System
Binary Number System to other Number System
Online Tool

# Converting binary numbers to other number systems

The binary number system is a positional number system with base 2 . In this number system, numbers are written using two symbols: 0 and 1.

May 07, 2023 By Arun Garg

Entrepreneur I Writer A binary digit is called a bit . The binary number system is the main system for representing information in computer memory. For more information about the mathematical tools and operations, please visit CoachingSelect.

### Converting binary numbers to decimal

Acceptable, given a binary number 1100012  To convert to decimal, write it as a sum over the digits as follow

1.25 + 1.24  + 0.23 + 0.22 + 0.21 + 1.20 = 49.

Same thing a little different:

1.32 + 1.16 + 0.8 + 0.4 + 0.2 + 1.1 = 49.

You can write this in tabular form as follows:

 512 256 128 64 32 16 8 4 2 1 1 1 0 0 0 1 +32 +16 +0 +0 +0 +1

Move from right to left. Under each binary unit, write its equivalent on the line below. Add the resulting decimal numbers. So the binary number 1100012 equals decimal 4910.

To convert from binary to decimal, use the following table of base 2 powers:

 1024 512 256 128 64 32 16 8 4 2 1

Converting from binary to octal and hexadecimal number systems

If you need to translate directly between binary and octal, binary and hexadecimal number systems, you can use a special scheme for quickly converting numbers.

In this case, the following rules are used: each octal digit can be written as three binary ( triad ), each hexadecimal digit can be written as four binary ( tetrad ). If the number of binary digits is not a multiple of three (four), then the number is optionally padded with insignificant zeros on the left. Use an online binary code translator to translate binary numbers into characters easily and quickly.

### Table of octal numbers:

X10               X8                            X2

 0 0 000 1 1 001 2 2 010 3 3 011 4 4 100 5 5 101 6 6 110 7 7 111

Hex table:

X10                  X16                            X2

 0 0 0000 1 1 0001 2 2 0010 3 3 0011 4 4 0100 5 5 0101 6 6 0110 7 7 0111 8 8 1000 9 9 1001 10 A 1010 11 B 1011 12 C 1100 13 D 1101 14 E 1110 15 F 1111

Converting binary fractions to decimals

Need to translate a number 1011010, 1012  to the decimal system. Let's write this number like this-

1.26+ 0.25  + 1.24 + 1.23 + 0.22 + 1.21  0.20+ 1.2-1  + 0.2-2 + 1.2-3 = 90,625.

Or according to the table:

 64 32 16 8 4 2 1 0.5 0.25 0.125 1 0 1 1 0 1 0 1 0 1 +64 +0 +16 +8 +0 +2 +0 0.5 0 0.125