Number Systems

Base 10: Decimal

Only 10 digits exist in the system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Used commonly in math, is the default representation of numbers in Java

Base 2: Binary

Only uses two digits, 0 and 1

Storing Binary in Java

To store binary in Java, the 0b header is used to indicate binary

int x = 0b100110;

Recursively Converting Decimal to Binary

int decimalToBinary(int decimal) {
    if (decimal == 0) return 0;
  return decimalToBinary(decimal / 2) * 10 + decimal % 2;
}

Base 2 Storage Units

Bit

The state of a single bit of memory, whether its 0 or 1.

Byte

8 bits

Kilobyte (KB)

1,024 Bytes

Megabyte (MB)

1,024 KB

Gigabyte (GB)

1,024 MB

Base 8: Octal

Only 8 digits within the system: 0, 1, 2, 3, 4, 5, 6, 7

Storing Octal in Java

To store octal in Java, the 0 header is used

int x = 0384;

Converting Decimal to Octal

Similar to Recursively Converting Decimal to Binary, we use the 8 digits instead of 2

int decimalToOctal(int decimal) {
    if (decimal == 0) return 0;
    return decimalToOctal(decimal / 8) * 10 + decimal % 8;
}

Base 16: Hexadecimal

Only 16 digits in the system: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Tip

Hexadecimal uses characters A-F to represents 10-15, respectively

Storing Hexadecimal in Java

To store hexadecimal in Java, the 0x header is used

int x = 0x4CB3;

Converting Decimal to Hexadecimal

String getHexString(int decimal) { // Map hex string to 
    switch (decimal) {
        case 10: return "A";
        case 11: return "B";
        case 12: return "C";
        case 13: return "D";
        case 14: return "E";
        case 15: return "F";
    }
    return Integer.toString(decimal);
}

String decimalToHex(int decimal) {
    if (decimal == 0) return ""; // Will result in empty string if decimal = 0
    return decimalToHex(decimal / 16) + getHexString(decimal % 16);
}