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Binary Math

Binary numbers and mathematics.

Decimal Conversion


**A decimal-to-binary and binary-to-decimal converter can be found at the bottom of this page. Simply enter the number you wish to convert, and the converter code will also explain the conversion process.**


Decimal to binary

 follows a straightforward method. It involves dividing the number to be converted, say N, by 2 (since binary is in base 2), and making note of the remainder. We continue dividing the quotient (N / 2) by 2, until we reach the division of (1 / 2), also making note of all remainders.

Example 1: Convert 98 from decimal to binary.

1) Divide 98 by 2, making note of the remainder. Continue dividing quotients by 2, making note of the remainders. Also note the star (*) beside the last remainder.

Division Remainder, R
98 / 2 = 49 R=0
49 / 2 = 24 R=1
24 / 2 = 12 R=0
12 / 2 = 6 R=0
6 / 2 = 3 R=0
3 / 2 = 1 R=1
1 / 2 = 0 R=1*

2) The sequence of remainders going up gives the answer. Starting from 1*, we have 1100010. Therefore, 98 in decimal is 1100010 in binary.

Example 2: Convert 21 into binary.

Division Remainder, R
21 / 2 = 10 R=1
10 / 2 = 5 R=0
5 / 2 = 2 R=1
2 / 2 = 1 R=0
1 / 2 = 0 R=1

Therefore, 21 in decimal is 10101 in binary.


Binary to decimal

  conversion follows the same steps as decimal to binary, except in reverse order. We begin by multiplying 0 x 2 and adding 1. We continue to multiply the numbers in the "results" column by 2, and adding the digits from left to right in our binary number.

Example 1: Convert 11101 from binary to decimal.

Operations Result
0 x 2 + 1 1
1 x 2 + 1 3
3 x 2 + 1 7
7 x 2 + 0 14
14 x 2 + 1 29

Therefore, 11101 in binary is 29 in decimal.


Decimal-to-binary converter

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Binary-to-decimal converter

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Binary Numbers | Add & Subtract | Multiply & Divide | Exercises | Conversion