Decimal to Binary Converter

To convert Decimal to Binary, input decimal value in the box below, and then click on the big blue button that says “CONVERT TO BINARY” and your binary is generated, copy it or you can download output file.

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Decimal Numbering System

In decimal number system there only ten (10) digits from 0 to 9. Every number (value) in this decimal system represents with 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. The base of this number system is 10, because it has only 10 digits.

Example: 8062 in decimal (base 10)

806210 = (8 x 103) + (0 x 102) + (6 x 101) + (2 x 100)

Binary Numbering System

In Binary number system there are only two digits that are 0 and 1. In this number system every number (value) represents with 0 and. The base of binary number system is 2, because it has only two digits.

Example: What is (110)2 in base 10?

1102 = (1 x 22) + (1 x 21) + (0 x 10) = 610

Decimal to binary Conversion:

To convert a number in decimal to a number in binary we have to divide the decimal number by 2 repeatedly, until the quotient of zero is obtained. This method of repeated division by 2 is called the ‘double-dabble’ method. The remainders are noted down for each of the division steps. Then the column of the remainder is read in reverse order i.e., from bottom to top order. We try to show the method with an example shown in Examples.

Example 1: Convert (26)10 into a binary number

Division Quotient Remainder
26/2 13 0
13/2 6 1
6/2 3 0
3/2 1 1
1/2 0 1

Hence the converted binary number is (11010)2

Example 2: Convert (139)2 into binary number:

Division Quotient Remainder
139/2 69 1
69/2 34 1
34/2 17 0
17/2 8 1
8/2 4 0
4/2 2 0
2/2 1 0

Hence the converted binary number is (0001011)2

Decimal To Binary Conversion Chart:

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

The most practical application of number system is in computer system. All computer programming and languages are based on 2-digit number system used in Digital Encoding (A process of using various patterns of voltage or current levels to represent 1s and 0s of the digital signals on the transmission link).