Convert decimal fractions to binary and vice versa with detailed step-by-step explanations.
2026-03-28T00:00:00Z
Binary fractions are fractional numbers represented in base-2 (binary) notation, just like decimal fractions are represented in base-10. In binary fractions, each digit to the right of the binary point represents a negative power of 2.
For example, in the binary fraction 0.101:
Binary fractions are essential in computer science and digital electronics because computers store and process all numbers in binary format, including fractional values (floating-point numbers).
No. Only fractions that can be expressed as a sum of powers of 2 (like 0.5, 0.25, 0.75) can be exactly represented. Others like 0.1 or 0.3 result in repeating binary fractions.
Because 0.1 and 0.2 cannot be exactly represented in binary. They're stored as approximations, and when added, the rounding errors accumulate, resulting in 0.30000000000000004 instead of 0.3.
For most purposes, 20 binary digits is sufficient. In practice, computers use 23 bits for float (32-bit) and 52 bits for double (64-bit) precision floating-point numbers.
Just like in decimal, you can get arbitrarily close to 1.0 (but never reach it with only fractional digits). For example, 0.111111... in binary approaches 1.0.
Use a sign bit (like in floating-point representation), or use two's complement for the entire number including the fractional part.
Floating-point numbers are a way to represent very large and very small numbers in binary using scientific notation: sign × mantissa × 2^exponent.
Yes! Convert the integer part (3 = 11 in binary) and fractional part (0.625 = 0.101 in binary) separately, then combine them: 11.101
All data in computers is stored in binary. Understanding binary fractions helps explain precision issues, rounding errors, and why certain decimal numbers can't be stored exactly.