Programming Number Formats

Every programming language needs ways to represent numbers. 理解する integer types, floating-point formats, and number base notations helps you write correct code and avoid subtle bugs related to precision, overflow, and representation.

Integer Types

Fixed-Size Integers

Language Examples

• C/C++: int, long, int32_t, uint64_t
• Java: byte, short, int, long
• Rust: i8, i16, i32, i64, u8, u16, u32, u64
• Go: int8, int16, int32, int64

Floating-Point Numbers

IEEE 754 Standard

• float (32-bit): ~7 decimal digits precision
• double (64-bit): ~15-16 decimal digits precision

Structure

• Sign bit (1 bit)
• Exponent (8 or 11 bits)
• Mantissa/significand (23 or 52 bits)

The Famous Problem

0.1 + 0.2 = 0.30000000000000004

This happens because 0.1 and 0.2 can't be represented exactly in binary floating-point.

Number Base Notation by Language

*C: Binary literals added in C23; C++14 and Java 7+ support them.

JavaScript Numbers

Characteristics

• All numbers are 64-bit floating-point (IEEE 754)
• Safe integer range: ±9,007,199,254,740,991 (2⁵³-1)
• BigInt for larger integers (ES2020+)

Number Literals

let dec = 255;        // Decimal
let hex = 0xFF;       // Hexadecimal
let bin = 0b11111111; // Binary
let oct = 0o377;      // Octal
let big = 9007199254740992n; // BigInt

Gotchas

• 0.1 + 0.2 !== 0.3 (floating-point)
• parseInt('08') === 8 (fixed in modern JS)

Python Numbers

Characteristics

• Integers have arbitrary precision (no overflow)
• Floats are 64-bit IEEE 754
• Complex numbers built-in

Number Literals

dec = 255          # Decimal
hex_num = 0xFF     # Hexadecimal  
bin_num = 0b11111111  # Binary
oct_num = 0o377    # Octal
complex_num = 3+4j # Complex

Conversions

bin(255)  # '0b11111111'
hex(255)  # '0xff'
oct(255)  # '0o377'
int('FF', 16)  # 255

Arbitrary Precision Numbers

When Needed

• Cryptography (large keys)
• Financial calculations (exact decimal)
• Scientific computing (extreme precision)

Language Support

• Python: int (always arbitrary precision)
• JavaScript: BigInt (for integers)
• Java: BigInteger, BigDecimal
• C#: BigInteger, decimal

Example: JavaScript BigInt

const big = 9007199254740993n;
const result = big * 2n;  // Must use n suffix

Formatted Output

JavaScript

num.toString(2)   // Binary string
num.toString(16)  // Hex string
num.toFixed(2)    // 2 decimal places

Python

f"{255:b}"    # '11111111' (binary)
f"{255:x}"    # 'ff' (hex)
f"{255:08b}"  # '11111111' (padded)

C/C++

printf("%d", num);   // Decimal
printf("%x", num);   // Hex (lowercase)
printf("%X", num);   // Hex (uppercase)
printf("%o", num);   // Octal

Bitwise Operations

Available in most languages for integer types:

まとめ

Programming languages handle numbers through various types: fixed-size integers (int32, int64), floating-point (float, double), and arbitrary precision types (BigInt, BigDecimal). 理解する base notation (0b, 0o, 0x prefixes) and the limitations of each type—especially floating-point precision issues—helps avoid subtle bugs. When exact decimal arithmetic matters (finance, currencies), use specialized decimal types rather than floating-point.

関連記事

• Binary in Computing: How Computers Think in 1s and 0s
• Number Base Applications: Where Different Bases Are Used