Conversion result
1 resultEquivalent number systems
| System | Value |
|---|---|
| Binary | 101101 |
| Decimal | 45 |
| Octal | 55 |
| Hexadecimal | 2D |
| Base 3 | 1200 |
| Base 4 | 231 |
Result details
| Grouped bits | 10 1101 |
|---|---|
| Scientific notation | 4.5 × 10^1 |
| Engineering notation | 45 × 10^0 |
| Character | - (ASCII) |
| Fraction status | Exact at selected precision |
Calculator inputs
Version 1.0.0Step-by-step working
positional method| Binary digit | Position | Power of two | Contribution |
|---|---|---|---|
| 1 | 5 | 2^5 | 32 |
| 0 | 4 | 2^4 | 0 |
| 1 | 3 | 2^3 | 8 |
| 1 | 2 | 2^2 | 4 |
| 0 | 1 | 2^1 | 0 |
| 1 | 0 | 2^0 | 1 |
Each binary digit is multiplied by two raised to its positional exponent. Integer exponents begin at zero on the right. Fractional exponents begin at negative one after the binary point.
Choose sign-magnitude, one’s complement, or two’s complement to see a signed interpretation explanation.
Recent conversion history
Your browser history will appear here after conversions.
Example conversion table
| Binary | Decimal | Octal | Hexadecimal |
|---|---|---|---|
| 0 | 0 | 0 | 0 |
| 1 | 1 | 1 | 1 |
| 10 | 2 | 2 | 2 |
| 11 | 3 | 3 | 3 |
| 100 | 4 | 4 | 4 |
| 101 | 5 | 5 | 5 |
| 1000 | 8 | 10 | 8 |
| 1010 | 10 | 12 | A |
| 1111 | 15 | 17 | F |
| 10000 | 16 | 20 | 10 |
| 11111111 | 255 | 377 | FF |
How to use this calculator
Enter a binary value
Type an integer, fraction, or grouped pattern. Valid digits are zero and one. Spaces, commas, underscores, and a leading 0b prefix are accepted. The calculator removes separators before processing. A single binary point may separate integer and fractional digits.
Select the interpretation
Unsigned mode treats every bit as a positive place value. Signed modes interpret the leading bit using sign-magnitude, one’s complement, or two’s complement rules. Select a bit width whenever a signed pattern is used. IEEE 754 mode decodes exact 16-bit, 32-bit, or 64-bit floating-point patterns.
Choose precision and grouping
Fraction precision controls displayed decimal places. Rounding options include half up, half even, truncation, and away-from-zero rounding. Grouping formats long patterns as nibbles, bytes, words, or 32-bit chunks without changing the value.
Review every result
The answer panel shows decimal output, normalized input, mode, bit counts, and significant bits. Related tables show octal, hexadecimal, base-three, base-four, scientific notation, engineering notation, and character information where applicable. The position table explains each power-of-two contribution.
Process many values
Enable batch mode and place one value on each line. The calculator returns a comparison table for all entries. CSV export preserves structured results. PDF export creates a printable summary. Browser history lets you reuse recent single conversions without sending data elsewhere.
Understand the method
Binary is a positional system with base two. Moving left doubles place value. Moving right across the binary point halves place value. Signed encodings reuse the same bits but apply different interpretation rules. Practice builds confidence when reading binary data every day.
Frequently asked questions
How do I convert binary to decimal?
Multiply each binary digit by two raised to its position. Start with position zero at the rightmost integer digit. Add every contribution to obtain the decimal value.
Can binary numbers contain decimal points?
Yes. They use a binary point. Positions after it represent one-half, one-quarter, one-eighth, and smaller negative powers of two.
What is the decimal value of 1010?
The value is 10. Its active positions contribute eight and two. Adding those contributions gives ten.
How does two’s complement work?
A leading zero is nonnegative. A leading one is negative. For negative patterns, subtract two raised to the bit width from the unsigned value.
Can this calculator handle very large binary numbers?
Yes. Integer conversion uses decimal-string arithmetic instead of ordinary machine integers. The application accepts patterns containing up to 10,000 bits.
What differs between signed and unsigned binary?
Unsigned mode assigns value to every bit. Signed modes reserve or reinterpret the leading bit, allowing negative values within a fixed width.
Why are binary positions powers of two?
Binary has two symbols. Each move left multiplies place value by the base, which is two. Each move right divides it by two.
Can I convert binary into hexadecimal and octal?
Yes. The result section displays octal and hexadecimal equivalents automatically for standard integer conversions, alongside base-three and base-four values.