How to use Number Base Converter
Type a number into any field — binary (base 2), decimal (base 10), octal (base 8), or hexadecimal (base 16) — and all other fields update instantly. Binary accepts only 0s and 1s, octal accepts 0-7, decimal accepts standard integers, and hex accepts 0-9 and A-F (case-insensitive). The ASCII reference table below the converter shows the character corresponding to each decimal value 32-127, useful for character encoding work.
Why use UtilDaily’s Number Base Converter?
- Developers switch between binary, hex, octal, and decimal constantly — for bitwise operations, memory addresses, color codes, and Unix permissions — this converts all four simultaneously from any starting base.
- Eliminates manual arithmetic that introduces errors when chaining base conversions (binary → decimal → hex).
- ASCII reference table maps each decimal value 32-127 to its character, useful for encoding work, debugging string byte values, and understanding ASCII art.
Frequently Asked Questions
How do I convert binary to decimal?
Multiply each binary digit by 2 raised to its position (starting from 0 on the right) and sum the results. For binary 1011: (1×2³) + (0×2²) + (1×2¹) + (1×2⁰) = 8 + 0 + 2 + 1 = 11. Binary 1111 1111 = 255 (which is 0xFF in hex). Type any binary number into the Binary field of this converter and the decimal value appears instantly.
How do I convert decimal to hex?
Divide the decimal number by 16 repeatedly, recording the remainder at each step. The remainders read in reverse give the hex digits. For decimal 255: 255 ÷ 16 = 15 remainder 15 (F); 15 ÷ 16 = 0 remainder 15 (F). Reading remainders in reverse: FF. So 255 decimal = FF hex = 11111111 binary. This calculator handles the conversion automatically — just type in the decimal field.
What is hexadecimal used for in programming?
Hexadecimal is widely used in programming because each hex digit represents exactly 4 bits, making it a compact representation of binary data. Common uses: CSS/HTML color codes (#FF5733), memory addresses (0x7FFFFFFF), byte values (0xFF = 255 = all 8 bits set), Unicode code points (U+0041 = 'A'), MAC addresses (00:1A:2B:3C:4D:5E), and file format magic bytes (JPEG files start with FF D8 FF). Hex is much easier to read than long binary strings.
What is a bitwise operation and why does binary matter?
Bitwise operations work directly on individual bits of integers. AND (&), OR (|), XOR (^), and NOT (~) compare or manipulate corresponding bits of two numbers. For example, 12 & 10 in binary: 1100 & 1010 = 1000 = 8 decimal. Bitwise operations are used in permissions systems (Unix uses 3-bit permissions: 7 = 111 = rwx), network masks, flags, and performance-sensitive code. Understanding binary is essential for working with bitwise operations correctly.
How do file permission numbers like 755 relate to binary?
Unix file permissions use octal (base 8). 755 in octal means: owner (7 = 111 in binary = read + write + execute), group (5 = 101 = read + execute), others (5 = 101 = read + execute). Common permission patterns: 644 (rw-r--r--) for files, 755 (rwxr-xr-x) for directories and executables, 600 (rw-------) for private files, 777 (rwxrwxrwx) for fully open. Type 755 into the Octal field of this converter to see the binary and decimal equivalents.
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