Number Base Converter

Number Base Converter

Number Bases Explained

• Binary (Base 2): Uses only digits 0 and 1. The fundamental language of computers — every piece of data is ultimately stored as binary bits (0 = off, 1 = on).
• Octal (Base 8): Uses digits 0–7. Historically used in computing as a shorthand for binary — each octal digit represents exactly 3 binary bits.
• Decimal (Base 10): The standard human number system using digits 0–9. All everyday arithmetic uses base 10.
• Hexadecimal (Base 16): Uses digits 0–9 and letters A–F. Widely used in programming, HTML colour codes, memory addresses, and byte representation — each hex digit represents exactly 4 binary bits.

Why Hexadecimal in Programming?

Hexadecimal is favoured in programming because it compactly represents binary data — one hex digit maps to exactly 4 bits (a nibble), so a full byte (8 bits) needs only two hex digits. For example, the byte 11111111 in binary is FF in hex — much easier to read and write in code, memory dumps, and colour values like #FF5733.

Quick Conversion Tricks

• Binary → Hex: Group binary digits in sets of 4 from the right. Each group of 4 maps to one hex digit (0000=0, 1111=F).
• Binary → Octal: Group binary digits in sets of 3 from the right. Each group of 3 maps to one octal digit.
• Decimal → Binary: Repeatedly divide by 2, noting the remainder each time. Read remainders bottom-to-top.
• Powers of 2: 2⁰=1, 2¹=2, 2²=4, 2³=8, 2⁴=16, 2⁵=32, 2⁶=64, 2⁷=128, 2⁸=256, 2¹⁰=1024 (1 KB).

Bitwise Operations

• AND (&): Result bit is 1 only if both input bits are 1. Used for masking.
• OR (|): Result bit is 1 if either input bit is 1. Used for setting flags.
• XOR (^): Result bit is 1 if the two input bits differ. Used for toggling and encryption.
• NOT (~): Flips all bits. In most languages, ~n = -(n+1) due to two's complement representation.