Decimal to Binary Converter

What is Decimal to Binary Conversion?

Decimal to binary conversion changes a base-10 number (digits 0-9) into its base-2 equivalent (only 0 and 1). Computers store and process all data in binary, so converting decimal to binary is the basis for understanding how a number is actually represented in memory.

For example, decimal 255 breaks down as (2×10²) + (5×10¹) + (5×10⁰). The same value in binary is 11111111, which is (1×2⁷) + (1×2⁶) + (1×2⁵) + (1×2⁴) + (1×2³) + (1×2²) + (1×2¹) + (1×2⁰). To convert the other direction, use the Binary to Decimal Converter. For arithmetic on binary values, see the Binary Calculator. For a broader look at how the two number systems compare, see binary vs decimal.

How to Convert Decimal to Binary Manually

The standard manual method is repeated division by 2:

Worked example: convert 42 to binary

42 ÷ 2 = 21 remainder 0
21 ÷ 2 = 10 remainder 1
10 ÷ 2 = 5  remainder 0
 5 ÷ 2 = 2  remainder 1
 2 ÷ 2 = 1  remainder 0
 1 ÷ 2 = 0  remainder 1

Reading remainders from bottom to top: 101010

Therefore, 42 in decimal = 101010 in binary

Manual division is useful for understanding the mechanics, but it is easy to drop a remainder on longer numbers — the converter above returns the exact result for any size of input. For a deeper walkthrough with more worked examples, the powers-of-two method, and common mistakes to avoid, see How to Convert Decimal to Binary.

Binary Place Value (Powers of Two)

Each binary digit (bit) represents a power of two based on its position, counting from the right starting at 2⁰. Summing the place values of every position holding a 1 gives the decimal equivalent — for example, 101010 has 1s in the 2⁵, 2³, and 2¹ positions: 32 + 8 + 2 = 42.

Decimal to Binary Conversion Table

A quick reference for common decimal numbers and their binary, hexadecimal, and octal equivalents:

Where Decimal to Binary Conversion Is Used

• Computer science education: understanding how numbers map between bases is foundational before moving on to logic gates, data structures, and low-level programming.
• Programming and debugging: bitwise operations, bit masks, and flag values are easier to reason about once a decimal value's binary form is visible.
• Digital electronics: binary is the native representation for logic circuits, registers, and memory addressing.
• Networking: IP addresses and subnet masks are groups of decimal octets that are easier to work with once expressed in binary. The Decimal to Hex Converter covers the related base-16 conversion used in areas like MAC addresses.

Negative Numbers and Two's Complement

This converter accepts zero and positive integers only. Simply writing a minus sign in front of a binary string (for example, -101010) isn't how computers represent negative numbers, and it isn't a fixed, unambiguous format on its own.

Machines represent negative numbers in binary using two's complement, which requires choosing a fixed bit width (such as 8, 16, or 32 bits) before the conversion makes sense. Use the Two's Complement Calculator to convert a negative decimal value into its signed binary representation at a specific bit width.

Related Converters

Frequently Asked Questions