Number Base Converter
Each base change keeps the value and rewrites the digits: 45.625 in binary is 101101.101.
Integers or fractions, e.g. 101101.101, 2D.A or 45.625; a minus sign is allowed.
101101.101
- Octal
- 55.5
- Decimal
- 45.625
- Hexadecimal
- 2D.A
- Binary grouped in fours
- 10 1101.101
Step-by-step solution
- Integer part: divide repeatedly by the target base and read the remainders bottom-up
- Fraction part: multiply repeatedly by the target base and read the integer parts top-down
- Shortcut: one hex digit = 4 bits, one octal digit = 3 bits
Number Base Converter Formula
N = Σ dᵢ·bⁱ
integer part: repeated division; fraction: repeated multiplication by the base
Worked Example
The decimal number 45.625:
- Integer part: divide repeatedly by the target base and read the remainders bottom-up
- Fraction part: multiply repeatedly by the target base and read the integer parts top-down
- Shortcut: one hex digit = 4 bits, one octal digit = 3 bits
Decimal: 45.625 · Hexadecimal: 2D.A · Binary grouped in fours: 10 1101.101
GATE tip
Number-system questions in GATE often hide an unknown base, e.g. (123)ₓ = (38)₁₀. Expand x² + 2x + 3 = 38 and solve; check with this converter using the “other base” option.
More Digital Logic and Number Representation Calculators
-
Two’s Complement Calculator
−x = invert(x) + 1
n-bit range −2ⁿ⁻¹ … 2ⁿ⁻¹ − 1
Example: −45 as an 8-bit number: 8-bit two’s complement = 1101 0011.
-
IEEE 754 Floating Point Converter
value = (−1)ˢ × 1.m × 2^(e − bias)
single: 8-bit exponent, bias 127, 23-bit mantissa; double: 11, 1023, 52
Example: −12.375 in single precision: IEEE 754 single (hex) = 0xC1460000.
-
K-Map Solver
F = Σm(…) + d(…) → minimal SOP / POS
Quine–McCluskey with an exact minimum cover
Example: F(A, B, C, D) = Σm(0, 1, 2, 5, 6, 7, 8, 9, 10, 14): Minimal SOP: F(A, B, C, D) = B′C′ + CD′ + A′BD.
Frequently asked questions
How do I convert binary to hexadecimal quickly?
Group the bits in fours from the point outwards and replace each group with its hex digit: 1011 0101 = B5.
Why does 0.1 never end in binary?
0.1 = 1/10 and 10 has the factor 5, so the binary fraction repeats (0.000110011…); that is why 0.1 + 0.2 ≠ 0.3 exactly in floating point.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Number Base Converter. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/number-base-converter/
IEEE
Scientific Converters, "Number Base Converter," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/number-base-converter/