Below, you may find information for how to convert from decimal to binary and how to convert from binary to decimal, including example conversions.
How to convert decimal to binary?
To convert decimal to binary, divide the decimal number by 2 repeatedly until the quotient is 0 and get the remainder for each iteration. These are the steps to convert decimal to binary:
1 - Divide the decimal number by 2.
2 - Keep aside the remainder left (0 or 1).
3 - Get the integer quotient for the next iteration and repeat till you get the quotient value is 0.
4 - At the end, reverse the order of the remainders to get the binary number.
For example, this is the step by step conversion of decimal number "18" to binary:
1 - 18 / 2
2 - Quotient (9), Remainder (0)
3 - 9 / 2
4 - Quotient (4), Remainder (1)
5 - 4 / 2
6 - Quotient (2), Remainder (0)
7 - 2 / 2
8 - Quotient (1), Remainder (0)
9 - 1 / 2
10 - Quotient (0), Remainder (1)
11 - Reverse the remainders 0, 1, 0, 0, 1
12 - 18 = 10010
Please visit base converter to convert between all number bases.
How to convert binary to decimal?
To convert from binary to decimal (base-2 to base-10), working from right to left, multiply the binary digit (0 or 1) by the power of 2 of that digit's location and add all at the end.
The power starts from 0 for the last binary digit. Increase that power by 1 for each next binary digit as you go to the left.
For example, these are the steps to convert binary number "10101" to decimal:
10101 = (1 * 2^{4}) + (0 * 2^{3}) + (1 * 2^{2}) + (0 * 2^{1}) + (1 * 2^{0})
10101 = 16 + 0 + 4 + 0 + 1
10101 = 21
What is Decimal Numeral System?
Decimal numeral system is base-10 numeral system that uses 10 decimal digits (0,1,2,3,4,5,6,7,8,9) to represent values from "0"–"9".
To convert between hex and decimal numbers, please visit hex to decimal converter.
What is Binary Numeral System?
Binary system is base-2 numeral system that uses only "1" and "0" to represent any number.
To convert between hex and binary numbers, please visit hex to binary converter.