Decimal to Binary Converter

How to Convert Decimal (Base-10) to Binary (Base-2)

The decimal numeral system (base-10) is the universal numbering system used in everyday life, relying on ten distinct digits: 0 through 9. In contrast, digital computer circuits operate using the binary system (base-2), representing all data using only two states: 0 (off) and 1 (on).

Method 1: The Successive Division by 2 Algorithm

The most common mathematical method to convert a decimal number to binary is successive division by 2 with remainders:

1. Divide the decimal number by 2.
2. Write down the whole quotient and record the remainder (0 if even, 1 if odd).
3. Take the quotient and divide by 2 again, recording the new remainder.
4. Repeat this process until the quotient becomes 0.
5. Read remainders from bottom to top (most significant bit to least significant bit).

Worked Example: Convert Decimal 156 to Binary

Division Steps:
156 ÷ 2 = 78  Remainder 0  (LSB - Rightmost bit)
 78 ÷ 2 = 39  Remainder 0
 39 ÷ 2 = 19  Remainder 1
 19 ÷ 2 =  9  Remainder 1
  9 ÷ 2 =  4  Remainder 1
  4 ÷ 2 =  2  Remainder 0
  2 ÷ 2 =  1  Remainder 0
  1 ÷ 2 =  0  Remainder 1  (MSB - Leftmost bit)

Read remainders from bottom to top:
Result: 156 (Decimal) = 10011100 (Binary)

Decimal to Binary Conversion Reference Table (1 to 20)

Quick lookup table for fundamental decimal numbers and their binary, hexadecimal, and octal equivalents:

Practical Applications in Computing

• Bitmasking & Permissions: Unix file permissions (such as chmod 755) use binary bitmasks to control read, write, and execute flags.
• Memory Addressing & Data Structures: Array indexing and hardware offsets are calculated in base-10 and converted to binary/hex by compilers.
• Reversing Conversions: Translate binary back to base-10 with our Binary to Decimal Converter, or convert numbers to base-16 with the Binary to Hex Converter.