A Number Bases Converter is a tool that converts numbers from one numeral system to another. Different numeral systems, or number bases, are commonly used for representing numbers, such as the decimal system (base 10), binary system (base 2), hexadecimal system (base 16), and others.
Common Number Bases:
Binary (Base 2): Uses digits 0 and 1.
Decimal (Base 10): Uses digits 0 to 9 (the most common system).
Octal (Base 8): Uses digits 0 to 7.
Hexadecimal (Base 16): Uses digits 0-9 and letters A-F (where A = 10, B = 11, ..., F = 15).
Conversion Between Number Bases:
Converting a number from one base to another involves either mathematical calculation or using a tool that handles the conversion for you. Here's how to convert between common bases:
1. Binary to Decimal:
To convert from binary (base 2) to decimal (base 10), you multiply each digit by 2 raised to the power of its position and sum the results.
Example: 1011₂ (binary) to decimal.
1 × 2³ + 0 × 2² + 1 × 2¹ + 1 × 2⁰
8 + 0 + 2 + 1 = 11₁₀
2. Decimal to Binary:
To convert from decimal to binary, divide the decimal number by 2 and keep track of the remainders. When the quotient is 0, the binary number is the remainders read from bottom to top.
Example: 11₁₀ to binary.
Divide 11 by 2 → Quotient: 5, Remainder: 1
Divide 5 by 2 → Quotient: 2, Remainder: 1
Divide 2 by 2 → Quotient: 1, Remainder: 0
Divide 1 by 2 → Quotient: 0, Remainder: 1
Binary = 1011₂
3. Hexadecimal to Decimal:
To convert from hexadecimal (base 16) to decimal, multiply each digit by 16 raised to the power of its position and sum the results.
Example: 2F₁₆ to decimal.
2 × 16¹ + 15 × 16⁰ (F = 15 in decimal)
32 + 15 = 47₁₀
4. Decimal to Hexadecimal:
To convert from decimal to hexadecimal, divide the decimal number by 16 and keep track of the remainders. When the quotient is 0, the hexadecimal number is the remainders read from bottom to top.
Example: 47₁₀ to hexadecimal.
Divide 47 by 16 → Quotient: 2, Remainder: 15 (F in hexadecimal)
Divide 2 by 16 → Quotient: 0, Remainder: 2
Hexadecimal = 2F₁₆
5. Binary to Hexadecimal:
You can group binary digits in sets of four (starting from the right) and convert each group to a hexadecimal digit.
Example: 10111010₂ to hexadecimal.
Group: 1011 1010
Convert each group: 1011₂ = B₁₆, 1010₂ = A₁₆
Hexadecimal = BA₁₆
6. Hexadecimal to Binary:
Each hexadecimal digit can be converted to a 4-bit binary equivalent.
Example: A3₁₆ to binary.
A = 1010₂, 3 = 0011₂
Binary = 10100011₂
Example of a Number Base Converter:
If you provide a number and the base you want to convert from and to (e.g., from binary to decimal or decimal to hexadecimal), I can perform the conversion for you.