Number Base Converter

What is hexadecimal and why is it used in programming?

Hexadecimal (base 16) uses digits 0–9 and letters A–F. Each hex digit represents exactly 4 binary bits (a nibble), making it a compact shorthand for binary. Programmers use it for memory addresses, color values (like #FF5733), bitfield masks, and low-level data where the underlying bit pattern matters. Two hex digits (00–FF) represent one byte.

How do I convert binary to decimal?

Multiply each binary digit by its positional power of 2, then sum them. For example, 1011 in binary = 1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8 + 0 + 2 + 1 = 11 in decimal. This converter does it instantly — just type the binary value in the Binary field.

What is octal used for?

Octal (base 8) is most commonly used for Unix file permissions. The command chmod 755 uses octal: 7 = rwx (read/write/execute), 5 = r-x (read/execute), so 755 = owner can do everything, group and others can read and execute. Each octal digit represents exactly 3 binary bits.

What does 0xFF mean?

0xFF is hexadecimal for 255 in decimal, or 11111111 in binary. It represents a byte with all 8 bits set to 1. It is commonly used as a bitmask to extract the lowest byte from a larger integer: value & 0xFF gives you the last 8 bits. In CSS colors, #FFFFFF means all three channels (R, G, B) are at maximum (255).

How do I convert hex to binary?

Each hexadecimal digit maps directly to exactly 4 binary bits: 0=0000, 1=0001, …, 9=1001, A=1010, B=1011, C=1100, D=1101, E=1110, F=1111. So 0xAF = 1010 1111 in binary. This makes hex a convenient shorthand for binary — just convert each digit individually.

What is two's complement / signed integers?

In signed 32-bit integers, the highest bit (bit 31) is the sign bit. If it is 1, the number is negative. The negative value is calculated as (unsigned value) − 2^32. For example, 0x80000000 = 2147483648 unsigned, but −2147483648 in signed 32-bit. This converter shows the signed interpretation when the 32-bit sign bit is set.