Decimal to Binary Converter

Convert decimal numbers to binary by inputting a decimal value and pressing the convert button.

Information on Number Conversion

A number system is a method of expressing numbers in a consistent manner using digits and numbers. There are different number system like, Decimal, Binary, Octal, Hexadecimal. These different number systems are used in different contexts.

Decimal Number System

Decimal number system is the most commonly used number system. It is a base 10 number system. It uses 10 digits from 0 to 9. The position of each digit in a decimal number denotes the power of 10. The rightmost digit is the ones place, the next digit to the left is the tens place, the next digit to the left is the hundreds place, and so on.

An example of a decimal number is
1234₁₀ = 1×10³ + 2×10² + 3×10¹ + 4×10⁰

Binary Number System

Binary number system is a base 2 number system. It uses only two digits, 0 and 1. The position of each digit in a binary number denotes the power of 2. The rightmost digit is the ones place, the next digit to the left is the twos place, the next digit to the left is the fours place, and so on.

An example of a binary number is
1011₂ = 1×2³ + 0×2² + 1×2¹ + 1×2⁰

How to convert Decimal to Binary?

To convert a decimal number to binary, you can use the following steps:

Step 1: Write down the decimal number.

Step 2: Divide the decimal number by 2.

Step 3: Write down the remainder (0 or 1) and quotient.

Step 4: Repeat steps 2 and 3 with the quotient until the quotient is 0.

Example 1: Convert 1234₁₀ to (?)₂

Step 1: Write down the decimal number: 1234₁₀

Step 2-3: Make a table of the division of 1234 by 2:

Division by 2	Quotent	Remainder	Bit
\frac{1234}{2}	617	0	0
\frac{617}{2}	308	1	1
\frac{308}{2}	154	0	2
\frac{154}{2}	77	0	3
\frac{77}{2}	38	1	4
\frac{38}{2}	19	0	5
\frac{19}{2}	9	1	6
\frac{9}{2}	4	1	7
\frac{4}{2}	2	0	8
\frac{2}{2}	1	0	9
\frac{1}{2}	0	1	10
The binary Representation of (1234)₁₀ is (10011010010)₂

Example 2: Convert 123456₁₀ to (?)₂

Step 1: Write down the decimal number: 123456₁₀

Step 2-3: Make a table of the division of 123456 by 2:

Division by 2	Quotent	Remainder	Bit
\frac{123456}{2}	61728	0	0
\frac{61728}{2}	30864	0	1
\frac{30864}{2}	15432	0	2
\frac{15432}{2}	7716	0	3
\frac{7716}{2}	3858	0	4
\frac{3858}{2}	1929	0	5
\frac{1929}{2}	964	1	6
\frac{964}{2}	482	0	7
\frac{482}{2}	241	0	8
\frac{241}{2}	120	1	9
\frac{120}{2}	60	0	10
\frac{60}{2}	30	0	11
\frac{30}{2}	15	0	12
\frac{15}{2}	7	1	13
\frac{7}{2}	3	1	14
\frac{3}{2}	1	1	15
\frac{1}{2}	0	1	16
The binary Representation of (123456)₁₀ is (11110001001000000)₂

Decimal to Binary conversion table

The table below shows the binary representation of decimal numbers from 0 to 16.

Decimal	Binary
0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001
10	1010
11	1011
12	1100
13	1101
14	1110
15	1111
16	10000