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2.3 Radix (Base)

Computers are electronic devices capable of processing only 0s and 1s. However, in our daily lives, we use the base-10 (Decimal) system. Therefore, to understand variables more deeply, it is important to know how computers store and read values.

1. Understanding Number Bases​

Base-10 (Decimal): Represents numbers using ten digits from 0 to 9. Base-2 (Binary): Represents numbers using only two digits, 0 and 1. This is the format computers use. Base-8 (Octal): Uses eight digits, from 0 to 7. (Rarely used recently) Base-16 (Hexadecimal): Represents numbers using the ten digits 0 to 9 plus the six letters A through F (A=10, F=15).

graph TD
A[Decimal: 15] --> B[Binary: 1111]
A[Decimal: 15] --> C[Octal: 17]
A[Decimal: 15] --> D[Hexadecimal: F]

2. Using Various Base Literals in Java​

Within Java source code, you can store binary, octal, and hexadecimal literals in variables. Java designates values with special prefixes to distinguish between different bases.

  • Decimal: No prefix
  • Binary: Prefix 0b or 0B
  • Octal: Prefix 0
  • Hexadecimal: Prefix 0x or 0X

Examples of Using Base Literals​

int decNum = 10;          // Decimal format (Value: 10)
int binNum = 0b1010;      // Binary format (Value: 10)
int octNum = 012;         // Octal format (Value: 10)
int hexNum = 0xA;         // Hexadecimal format (Value: 10)

System.out.println(decNum);
System.out.println(binNum); // All output internally as decimal
System.out.println(octNum);
System.out.println(hexNum);

3. Bit and Byte​

  • bit: The most basic unit of data for a computer. Either 0 or 1.
  • byte: A unit of 8 bits combined. 1 byte = 8 bit.

The smallest unit among Java's integer types is 1 byte (the byte type), which can store values ranging from -128 to 127. Using a 2-digit hexadecimal number clearly represents a value of exactly 1 byte, making it commonly used. (0xFF == 255)

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