Convert decimal integers to binary with a step-by-step division-by-two breakdown showing quotients, remainders, and the final binary string.
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The decimal to binary converter translates decimal (base-10) integers into their binary (base-2) equivalents. Enter a decimal number and see the binary result with a step-by-step division breakdown.
Repeatedly divide the decimal number by 2 and record the remainder at each step. The binary result is the sequence of remainders read from bottom to top (last remainder first).
For example, decimal 13 divided by 2 gives quotients 6, 3, 1, 0 with remainders 1, 0, 1, 1, producing binary 1101.
Repeat: quotient = n div 2, remainder = n mod 2
Divide by 2 repeatedly, collecting remainders, until the quotient reaches 0.
Converting decimal to binary is essential when working with bitwise operations, setting hardware registers, understanding memory layout, or preparing values for digital logic circuits.
Frequently asked questions
This converter handles integers. Decimal fractions are converted by repeatedly multiplying by 2 and extracting the integer part, which can produce a non-terminating binary expansion.
Convert the binary result back to decimal by summing positional powers of 2. If it matches the original input, the conversion is correct.
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