Why do programmers use hexadecimal instead of binary?

Hexadecimal is more compact and readable while still mapping directly to binary. Each hex digit represents exactly 4 bits, so a byte (8 bits) is just 2 hex digits. Writing FF is much easier than 11111111, and both represent 255.

What's the largest number a byte can hold?

A byte (8 bits) can hold values from 0 to 255 (or -128 to 127 if signed). In binary that's 00000000 to 11111111, in hex it's 0x00 to 0xFF.

Why are file permissions in octal?

Unix permissions use 3 bits per category (read, write, execute), and octal digits represent exactly 3 bits. This makes octal a natural fit - each digit directly represents the permissions for owner, group, or others.

How do I know which base a number is in?

Look for prefixes: 0b for binary, 0o or leading 0 for octal, 0x for hex, no prefix for decimal. In CSS colors, # indicates hex. Context matters too - memory addresses are typically hex.

Why does hex use letters A-F?

Hex needs 16 symbols (0-15), but we only have 10 numeric digits. Letters A-F represent values 10-15. This keeps each position as a single character, making hex compact and easy to read.

Number Base Conversion: Developer Guide

Every number you see on screen is ultimately represented as binary in your computer's memory. Yet we use decimal for human interfaces, hexadecimal for colors and memory addresses, and octal for file permissions. Understanding number bases isn't just academic - it's essential for debugging, working with low-level code, and understanding how computers actually work. This guide explains the most important number bases and how to convert between them.

Understanding number bases

A number base (or radix) defines how many unique digits are used to represent numbers. Common bases: • Binary (Base 2): 0, 1 • Octal (Base 8): 0-7 • Decimal (Base 10): 0-9 • Hexadecimal (Base 16): 0-9, A-F The position of each digit determines its value: • In decimal 253: 2×100 + 5×10 + 3×1 • In binary 11111101: 128+64+32+16+8+4+0+1 = 253 • In hex FD: 15×16 + 13×1 = 253 Why different bases exist: • Binary: How computers actually store data • Octal: Compact binary (3 bits per digit), Unix permissions • Decimal: Human-friendly, our natural counting system • Hexadecimal: Compact binary (4 bits per digit), colors, memory

Binary: the computer's language

Everything in a computer is ultimately binary - ones and zeros representing electrical states (on/off). Binary basics: • Each digit is called a bit • 8 bits = 1 byte • Maximum byte value: 11111111 = 255 Common binary patterns: • 00000000 = 0 • 00000001 = 1 • 00001010 = 10 • 01100100 = 100 • 11111111 = 255 Why developers need binary: • Understanding bitwise operations (AND, OR, XOR) • Working with hardware and embedded systems • Network protocols and data structures • Debugging memory issues • Compression algorithms Binary prefixes: • In code: 0b prefix (0b1010 = 10) • Bit manipulation is incredibly fast • Powers of 2 are clean binary numbers

Hexadecimal: the developer's favorite

Hexadecimal (base 16) is everywhere in programming because it maps perfectly to binary - each hex digit represents exactly 4 bits. Hex digits: 0-9, then A=10, B=11, C=12, D=13, E=14, F=15 Common uses: Colors (RGB) • #FF0000 = Red (255, 0, 0) • #00FF00 = Green (0, 255, 0) • #FFFFFF = White (255, 255, 255) Memory addresses • 0x7FFE0000 (stack pointer) • Error messages often show hex addresses Character codes • ASCII 'A' = 0x41 = 65 • Unicode uses hex extensively Binary data • Byte values: 0x00 to 0xFF • SHA-256 hashes displayed in hex Hex prefixes: • 0x in most languages (0xFF) • # for CSS colors (#FF0000) • \x for escape sequences (\x41)

Octal: Unix permissions and beyond

Octal (base 8) is less common but crucial for Unix/Linux file permissions. Octal digits: 0-7 File permissions explained: • Read (r) = 4 • Write (w) = 2 • Execute (x) = 1 Permission combinations: • 7 (rwx) = 4+2+1 = read+write+execute • 6 (rw-) = 4+2 = read+write • 5 (r-x) = 4+1 = read+execute • 4 (r--) = read only Common permission sets: • 755 = rwxr-xr-x (owner full, others read/execute) • 644 = rw-r--r-- (owner read/write, others read) • 777 = rwxrwxrwx (full access to everyone - dangerous!) Other octal uses: • C escape sequences (\077 = ?) • Some legacy systems • Compact representation of 3-bit groups Octal prefix in code: Leading zero (0755)

Converting between bases

Manual conversion methods: Decimal to binary: 1. Divide by 2, note remainder 2. Repeat until quotient is 0 3. Read remainders bottom-to-top Example: 13 to binary 13÷2 = 6 r1 6÷2 = 3 r0 3÷2 = 1 r1 1÷2 = 0 r1 Result: 1101 Binary to hex (easy!): 1. Group binary digits in 4s from right 2. Convert each group to hex digit Example: 11111101 1111 1101 F D Result: FD Hex to binary: 1. Convert each hex digit to 4 binary digits Example: 2A 2 = 0010 A = 1010 Result: 00101010 Quick mental math: Powers of 2: 1, 2, 4, 8, 16, 32, 64, 128, 256...

Programming with different bases

Most languages support multiple bases natively: JavaScript: let binary = 0b1010; // 10 let octal = 0o12; // 10 let hex = 0x0A; // 10 num.toString(2); // to binary string parseInt('1010', 2); // from binary string Python: binary = 0b1010 # 10 octal = 0o12 # 10 hex_num = 0x0A # 10 bin(10) # '0b1010' oct(10) # '0o12' hex(10) # '0xa' int('1010', 2) # 10 Common operations: • Bitwise AND: a & b • Bitwise OR: a | b • Bitwise XOR: a ^ b • Left shift: a << n (multiply by 2^n) • Right shift: a >> n (divide by 2^n) Practical tip: When debugging, console.log with .toString(16) to see hex values.

Conclusion

Understanding number bases is fundamental to programming. Binary is how computers think, hexadecimal is how developers communicate binary compactly, octal handles Unix permissions, and decimal is for human interfaces. The key insight is that these are all different ways of representing the same values - 255, 0xFF, 0b11111111, and 0377 are identical numbers. Use our base converter tool to quickly convert between number systems and explore how different bases relate to each other.