Programming

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Basics / Number Systems

Decimal

An integer can be specified in decimal, base 10 
 
echo 10;    // 10
echo -1;    // -1
echo  0;    // 0
echo 1452;  // 1452

Octal

We use octal when we need a readable format for bit string in group of 3. 
 
rw-r--r-- = 110100100 (binary) = 644 (octal) # Unix access permision - 0755

READ (1) WRITE (1) EXEC (1) = binary 111 = octal 7
READ (1) WRITE (1) EXEC (0) = binary 110 = octal 6
READ (1) WRITE (0) EXEC (0) = binary 100 = octal 4

97 (decimal) = 141 (octal) # To convert decimal to octal, use modulus

97 % 8 => reminder 1
12 % 8 => reminder 4
1  % 8 => reminder 1

1*8^2 + 4*8^1 + 1*8^0 = 64 + 32 + 1 = 97

Binary

To conver binary to octal, convert first to decimal, then to octal. 
 
echo 0b110100100;           // 420 - decimal
echo bindec(110100100);     // 420 - decimal
echo decoct(0b110100100);   // 644 - octal

echo 0644;
    // 6*8^2 + 4*8^1 + 4*8^0
    // 384 + 32 + 4
    // 420

echo 0b1010111100;
    // 700
    // 001 010 111 100 
    // 00 are added to complete group of 3 bits
    // 001 010 111 100 (binary) = 1274 (octal)

Hexadecimal

Base 16 notation, identified by its leading 0x. 
 
/**
 * Hex numbers are often used to represent colours.
 * Orange is represented as #FFA500 (255 red, 165 green, 0 blue).
 */

echo 0x121;     // 1*16^2 + 2*16^1 + 1*16^0 = 256 + 32 + 1 = 289
echo 0xFF;      // 15*16^1 + 15*16^0 = 240 + 15 = 255

Float

Be aware that the float data type is not always capable of representing numbers. 
 
/**
 * Float data type is not always capable of representing numbers.
 * The result of this simple expression is stored internally as 7.999999
 */

echo (0.1 + 0.7) * 10; // 8
echo (int) ((0.1 + 0.7) * 10); // 7




References