Convert Decimal to Binary

Converting decimal to binary is the reverse of binary-to-decimal and is equally important for anyone working with computers. The most common technique is the repeated division by 2 method.

Step-by-step example — converting 42 to binary:

1. Divide 42 by 2: quotient = 21, remainder = 0
2. Divide 21 by 2: quotient = 10, remainder = 1
3. Divide 10 by 2: quotient = 5, remainder = 0
4. Divide 5 by 2: quotient = 2, remainder = 1
5. Divide 2 by 2: quotient = 1, remainder = 0
6. Divide 1 by 2: quotient = 0, remainder = 1

Read the remainders from bottom to top: 101010. So 42₁₀ = 101010₂.

Alternative method — subtraction of powers of 2:

Start with the largest power of 2 that fits into your number and subtract downward:

• 42 - 32(2⁵) = 10, write 1
• 10 - 16(2⁴)? No. Write 0
• 10 - 8(2³) = 2, write 1
• 2 - 4(2²)? No. Write 0
• 2 - 2(2¹) = 0, write 1
• 0 - 1(2⁰)? No. Write 0

Result: 101010₂. This subtraction method is often faster for mental arithmetic.

Practical tips:

• Round numbers like 64, 128, and 256 convert instantly because they are exact powers of 2.
• To convert a number like 255, recognize it is 2⁸ - 1, so the binary representation is eight 1s: 11111111.
• In programming, you can verify your result using parseInt("101010", 2) in JavaScript or int("101010", 2) in Python, both of which return 42.

Understanding decimal-to-binary conversion is critical for implementing hash functions, encoding data, and working with binary protocols.