Decimal to Binary Converter – Base 10 to Base 2

Decimal to binary conversion rewrites a base-10 integer as a base-2 string of bits.

It is the inverse of binary to decimal and is essential for understanding how CPUs store unsigned integers.

• Enter a decimal number.
• View binary output with or without Live mode.
• Copy/download the bit string for labs or documentation.
• Verify with the Binary to Decimal Converter.

• Each bit position corresponds to a power of two.
• The binary representation is unique for positive integers (ignoring leading zeros).
• Longer bit strings are needed for larger decimal values.

• Divide the decimal number by 2; write the remainder (0 or 1).
• Repeat with the quotient until the quotient is 0.
• Read remainders from last to first — that is your binary number.
• Example: 13 → 13÷2 r1, 6÷2 r0, 3÷2 r1, 1÷2 r1 → 1101₂.

Repeated division by 2 (equivalent to finding coefficients of powers of two):

• While n > 0: remainder = n mod 2; prepend remainder to answer; n = floor(n / 2).
• Or accumulate: largest power of two ≤ n, subtract, repeat.

• Registers and memory hold fixed-width bit patterns (8, 16, 32, 64 bits).
• Overflow occurs when a value needs more bits than the type allows.
• Hexadecimal is often used as a compact view of the same bits.

• Hardware switches are reliable in two states.
• Logic gates (AND, OR, NOT) map directly to binary algebra.
• All higher-level data (text, images) is ultimately stored as bits.

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