Decimal to Binary Short Division Step-by-Step Calculator

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Convert Decimal with Fraction to n-bit Unsigned Binary with Fraction Step-by-Step Calculator

Display Fraction Part as Binary Scientific Notation (e.g., 0.101011 * 2^-5)

Decimal to Binary Fraction Step-by-Step Calculator

Question Examples:

Question 1: Convert 4 + 0.00012 = 4.00012 to a 16-bit unsigned binary fraction

Answer:

Display Fraction Part as Binary Scientific Notation (e.g., 0.101011 * 2^-5)
Short Division Step-by-Step for Integer Part:
24 ...0
22 ...0
21 ...1
Binary for Integer Part:100
log(10-3)⁄log(2) ≈ - 10
10-3 ≈ 2-10 (near 1024)
0.00012 = 0.00012 × 210⁄210 = 0.12 × 10-3 × 210 = 0.12288 × 2-10
2-10 = 0.0000 0000 012
Multiple by 2 for Fraction Part:
0.12288 x 2 = 0.24576 ...0
0.24576 x 2 = 0.49152 ...0
0.49152 x 2 = 0.98304 ...0
0.98304 x 2 = 1.96608 ...1

Fraction Binary: 0001
(Fraction end at bit 4 due to digit overflow, all digit available if Fraction Binary Bit = 0)
0.0001210 = .00012 × 2-10 = 100.0000 0000 00 00012