How do you convert decimal to binary?

Divide the decimal number by 2 repeatedly, keeping track of the remainders. Read the remainders from bottom to top to get the binary representation. For example, to convert 13: 13÷2=6 remainder 1, 6÷2=3 remainder 0, 3÷2=1 remainder 1, 1÷2=0 remainder 1. Reading up: 1101.

What is the binary representation of decimal 10?

Decimal 10 in binary is 1010. You can verify: (1×2³) + (0×2²) + (1×2¹) + (0×2⁰) = 8 + 0 + 2 + 0 = 10.

How many bits do I need for a given decimal number?

For a positive integer n, you need ⌊log₂(n)⌋ + 1 bits. For example, to represent 255, you need 8 bits (2⁸ = 256, so 255 fits in 8 bits). For 1000, you need 10 bits.

Can I convert negative decimal numbers to binary?

Yes, but you need to specify the representation format. Common methods include sign-magnitude, one's complement, and two's complement. Two's complement is most common in modern computers. Our converter handles unsigned (positive) numbers by default.

Why is decimal to binary conversion important?

Computers store and process all data in binary format. Converting decimal to binary helps you understand how data is represented in memory, work with bitwise operations, configure hardware registers, and debug low-level code.

🔢 Decimal to Binary Converter

Convert decimal numbers to binary instantly. Free online decimal to binary converter with detailed steps for quick and accurate conversions.

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Conversion: Decimal → Binary

Converting decimal numbers to binary is a fundamental skill in computer science and digital electronics. Since computers process information in binary format, understanding how to convert human-readable decimal numbers to binary is essential for programming, hardware design, and system analysis. This converter provides instant, accurate conversions from decimal to binary representation.