Binary to Decimal and Decimal to IEEE 754 Converter
Binary to Decimal and Decimal to IEEE 754 Converter Tool
This online tool is designed to convert binary numbers to decimal and decimal numbers to IEEE 754 representation. It supports single precision (32-bit), double precision (64-bit), and half precision (16-bit) conversions, making it a valuable resource for students, developers, and engineers working with binary and decimal data.
Binary to Decimal Converter
Decimal to IEEE 754 Converter
How the Tool Works
The binary to decimal conversion is performed using the formula: decimal = βn-1 × d1 + βn-2 × d2 + … + β0 × dn, where β is the base of the number system (2 for binary) and d is the binary digit.
The decimal to IEEE 754 conversion is performed using the following steps:
- Determine the sign bit (1 for negative numbers, 0 for positive numbers)
- Calculate the exponent (biased by 127 for single precision, 1023 for double precision, and 15 for half precision)
- Calculate the mantissa (subnormal or normal)
- Combine the sign bit, exponent, and mantissa to form the IEEE 754 representation
Example Conversions
| Binary Input | Decimal Output |
|---|---|
| 1010 | 10 |
| 1101 | 13 |
| 10011 | 19 |
| Decimal Input | IEEE 754 Output (Single Precision) | IEEE 754 Output (Double Precision) | IEEE 754 Output (Half Precision) |
|---|---|---|---|
| 10.5 | 0 10000000 01000000000000000000000 | 0 10000000000 01000000000000000000000000 | 0 01101 0100 |
| 20.25 | 0 10000001 01010000000000000000000 | 0 10000000001 01010000000000000000000000 | 0 10010 0110 |
Common Use Cases for the Binary to Decimal and Decimal to IEEE 754 Converter Tool
- Computer programming: converting binary data to decimal for easier manipulation and vice versa
- Embedded systems: working with binary and decimal data in microcontrollers and other embedded devices
- Cryptography: converting binary data to decimal for encryption and decryption purposes
- Data analysis: converting decimal data to IEEE 754 representation for efficient storage and processing
- Scientific simulations: converting decimal data to IEEE 754 representation for accurate and efficient calculations
- Computer networking: converting binary data to decimal for packet analysis and network diagnostics
- Database management: converting decimal data to IEEE 754 representation for efficient storage and retrieval
- Machine learning: converting decimal data to IEEE 754 representation for efficient neural network computations
- Computer graphics: converting decimal data to IEEE 754 representation for efficient rendering and graphics processing
- Audio and video processing: converting decimal data to IEEE 754 representation for efficient audio and video processing