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Try an Example
Pick a scenario to see how the calculator works, then adjust the values
ASCII Letter A
Convert the ASCII code for uppercase A (65) across all bases.
Key values: Decimal 65 · Binary 1000001 · Hex 41
Byte Maximum
The largest value a single byte can hold (255).
Key values: Decimal 255 · Binary 11111111 · Hex FF
Hex Color Code
Convert a common hex color code (deep sky blue) to other bases.
Key values: Hex 00BFFF · Decimal 49151 · Binary nibbles
This calculator is also known as Binary Decimal Converter.
Read the complete guideBinary to Decimal
To convert binary to decimal, multiply each bit by its positional weight (powers of 2) and sum. For example, 1010 = 1*8 + 0*4 + 1*2 + 0*1 = 10.
Decimal to Binary
Use the repeated division method:
- Divide the number by 2
- Record the remainder (0 or 1)
- Replace the number with the quotient
- Repeat until the quotient is 0
- Read remainders from bottom to top
Examples
Decimal 57 to Binary
A CS student needs to convert 57 to binary for homework.
57/2=28 R1, 28/2=14 R0, 14/2=7 R0, 7/2=3 R1, 3/2=1 R1, 1/2=0 R1. Read bottom-up: 111001.
Key takeaway: 57 decimal = 111001 binary.
Binary 10110 to Decimal
Convert 10110 binary to decimal using positional notation.
1*16 + 0*8 + 1*4 + 1*2 + 0*1 = 22.
Key takeaway: 10110 binary = 22 decimal.
Byte Max Value
What is the largest value a byte (8 bits) can hold?
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255.
Key takeaway: 11111111 binary = 255 decimal, the maximum value of an unsigned byte.
Practicing Binary Conversion
Tips for mastering binary-decimal conversion:
- Memorize powers of 2 up to 2^10 = 1024
- Practice converting byte values (0-255)
- Use the doubling method for binary to decimal (Horner's method)
Frequently Asked Questions about Binary Decimal Converter
What is the fastest way to convert binary to decimal?
Memorize powers of 2 (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024...) and add the ones where the binary digit is 1.
Can binary numbers have decimal points?
Yes. Binary fractions use negative powers of 2. For example, 0.1 in binary = 1 * 2^(-1) = 0.5 in decimal, and 0.11 in binary = 0.75.
How many bits do I need to represent a given decimal number?
You need ceil(log2(N + 1)) bits. For example: 255 needs 8 bits, 256 needs 9 bits, and 1000 needs 10 bits.
Specialized Calculators
Choose from 6 specialized versions of this calculator, each optimized for specific use cases and calculation methods.
Conversion
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