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.
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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:
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:
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
X10 X16 X2
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: