Decimal to Binary Converter

Convert decimal (base-10) numbers to binary (base-2) instantly with a step-by-step division breakdown. Supports batch conversion and reverse direction.

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Decimal → Binary

Common Decimal to Binary Values

1
= 1
8
= 1000
10
= 1010
16
= 10000
42
= 101010
64
= 1000000
100
= 1100100
127
= 1111111
128
= 10000000
255
= 11111111
256
= 100000000
1024
= 10000000000

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Bidirectional

Convert decimal to binary and binary back to decimal. Click the Swap button to switch direction instantly.

Division Breakdown

See the full division-remainder method showing each step of converting a decimal number to binary.

Configurable Output

Pad to 4, 8, 16, or 32 bits. Group binary digits into 4-bit nibbles for easy reading.

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Frequently Asked Questions

How do I convert decimal to binary?
Use the division-remainder method: divide the decimal number by 2 repeatedly and record each remainder. Read the remainders from bottom to top. For example, 42 ÷ 2 = 21 r0, 21 ÷ 2 = 10 r1, 10 ÷ 2 = 5 r0, 5 ÷ 2 = 2 r1, 2 ÷ 2 = 1 r0, 1 ÷ 2 = 0 r1. Reading bottom-to-top: 101010.
What is binary?
Binary is a base-2 number system using only digits 0 and 1. It's the fundamental language of computers because digital circuits have two states: on (1) and off (0). Each binary digit is called a "bit", 8 bits make a "byte", and a byte can represent values from 0 to 255.
What is 255 in binary?
255 in binary is 11111111 (eight 1s). This is the maximum value stored in a single byte (8 bits). It appears commonly in RGB color values (e.g., rgb(255, 255, 255) for white), subnet masks, and as the max unsigned 8-bit integer.
What is the decimal to binary formula?
The division-remainder method: divide the number by 2 and note the remainder (0 or 1). Continue dividing the quotient by 2 until it reaches 0. The binary number is the remainders read from bottom to top. For large numbers, you can also use positional subtraction: find the largest power of 2 that fits, place a 1, subtract, and repeat.
Can I convert binary back to decimal?
Yes! Multiply each binary digit by 2 raised to the power of its position (starting from 0 on the right) and add the results. For example, 101010 = (1×32) + (0×16) + (1×8) + (0×4) + (1×2) + (0×1) = 42. Click "Swap Direction" to use this mode.