Base 16 Result
FF
Decimal
255
Base 10
255
Valid digits for base 10: 0–9
Supported bases: 2 (binary) through 36 (0-9 + A-Z)
FF
255
255
11111111
377
value = Σ(dᵢ × b^i) for i = 0 to n-1Convert any base to decimal by multiplying each digit by the base raised to its position power (counting from 0 at the rightmost digit), then summing all terms.
Where:
dᵢ= The digit at position ib= The base (radix) of the source numberi= Position index, starting at 0 from the rightn= Total number of digitsDivide by target base, collect remainders, read bottom-to-topRepeatedly divide the decimal number by the target base. Each remainder becomes a digit in the result. Read the remainders from last to first to get the converted number.
Where:
n= The decimal number to convertb= The target baser= Remainder at each step (becomes a digit in the result)Inputs
Result
255 ÷ 16 = 15 remainder 15. 15 ÷ 16 = 0 remainder 15. Remainders are 15 and 15, which map to F and F. Result: FF.
Inputs
Result
1×2⁴ + 0×2³ + 1×2² + 1×2¹ + 0×2⁰ = 16 + 0 + 4 + 2 + 0 = 22.
Inputs
Result
1A3 (hex) = 1×256 + 10×16 + 3×1 = 419 (decimal). Then 419 ÷ 8 = 52 R3, 52 ÷ 8 = 6 R4, 6 ÷ 8 = 0 R6. Read remainders: 643.
A number base (or radix) defines how many unique digits a positional number system uses. Base 10 (decimal) uses digits 0–9. Base 2 (binary) uses 0 and 1. Base 16 (hex) uses 0–9 and A–F. Each digit position represents a power of the base.
| Base | Name | Digits | Decimal 255 |
|---|---|---|---|
| 2 | Binary | 0, 1 | 11111111 |
| 8 | Octal | 0–7 | 377 |
| 10 | Decimal | 0–9 | 255 |
| 16 | Hexadecimal | 0–F | FF |
| 36 | Base-36 | 0–Z | 73 |
The standard method is two steps: first convert to decimal (base 10) by multiplying each digit by its positional power, then convert from decimal to the target base by repeatedly dividing and collecting remainders.
| From | To | Example Input | Result |
|---|---|---|---|
| Decimal → Binary | 10 → 2 | 255 | 11111111 |
| Binary → Hex | 2 → 16 | 11111111 | FF |
| Hex → Octal | 16 → 8 | FF | 377 |
| Octal → Decimal | 8 → 10 | 377 | 255 |
Programmers primarily use base 2 (binary), base 8 (octal), base 10 (decimal), and base 16 (hexadecimal). Binary maps directly to hardware bits. Hex is compact shorthand for binary (1 hex digit = 4 bits). Octal appears in Unix permissions.
| Use Case | Preferred Base | Example |
|---|---|---|
| CSS Colors | Hex (16) | #FF6600 |
| File Permissions | Octal (8) | chmod 755 |
| IP Addresses | Decimal (10) | 192.168.1.1 |
| Memory Dump | Hex (16) | 0x7FFF |
In positional notation, a number equals the sum of each digit multiplied by the base raised to its position. For example, 1A3 in base 16 = 1×16² + 10×16¹ + 3×16⁰ = 256 + 160 + 3 = 419 in decimal.
| Number | Base | Calculation | Decimal |
|---|---|---|---|
| 1010 | 2 | 8+0+2+0 | 10 |
| 77 | 8 | 7×8+7×1 | 63 |
| FF | 16 | 15×16+15×1 | 255 |
| 1A3 | 16 | 256+160+3 | 419 |
Yes. This calculator supports bases from 2 to 36. Bases above 10 use letters as digits: A=10, B=11, ... Z=35. Base 36 is the highest single-character base, using digits 0–9 and letters A–Z. Base 36 is used in URL shorteners and compact IDs.
| Base | Max Digit | Decimal 1000 In Base |
|---|---|---|
| 12 | B | 6B4 |
| 20 | J | 2A0 |
| 32 | V | V8 |
| 36 | Z | RS |
Number base conversion is a fundamental concept in computer science and mathematics. Every number system is defined by its base (or radix), which determines how many unique digits it uses and the value of each position.
The most common bases in computing are binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Converting between them is essential for tasks ranging from low-level programming to web design.
Our calculator supports any base from 2 to 36, showing both the converted result and a step-by-step breakdown of the positional notation calculation used to arrive at the answer.
Last Updated: Mar 9, 2026
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