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Fundamentals of Data Encoding, Big Endian, Little Endian
The processor can work with different types of data. These include integers of different sizes, floating point numbers, texts, structures and even single bits. All these data are stored in the memory as a single byte or multiple bytes. Integer data types can be 8, 16, 32 or 64 bits long. If the encoded number is unsigned it is stored in binary representation, while the value is signed the representation is two's complement. In two's complement representation, the most significant bit (MSB) represents the sign of the number. Zero means a non-negative number, one represents a negative value. The table 1 shows the integer data types with their ranges.
Table 1: Integer binary numbers
| Number of bits | Minimum value (hexadecimal) | Maximum value (hexadecimal) | Minimum value (decimal) | Maximum value (decimal) |
|---|---|---|---|---|
| 8 | 0x00 | 0xFF | 0 | 255 |
| 8 signed | 0x80 | 0x7F | -128 | 127 |
| 16 | 0x0000 | 0xFFFF | 0 | 65 535 |
| 16 signed | 0x8000 | 0x7FFF | -32 768 | 32 767 |
| 32 | 0x0000 0000 | 0xFFFF FFFF | 0 | 4 294 967 295 |
| 32 signed | 0x8000 0000 | 0x7FFF FFFF | -2 147 483 648 | 2 147 483 647 |
| 64 | 0x0000 0000 0000 0000 | 0xFFFF FFFF FFFF FFFF | 0 | 18 446 744 073 709 551 615 |
| 64 signed | 0x8000 0000 0000 0000 | 0x7FFF FFFF FFFF FFFF | -9 223 372 036 854 775 808 | 9 223 372 036 854 775 807 |
Integer calculations do not always cover all mathematical requirements of the algorithm. To represent real numbers the floating point encoding is used. A floating point is the representation of the value A which is composed of two numbers
- Mantissa (Ma)
- Exponent (Ea)
fulfilling the equation
There are two main types of real numbers, called floating point values. Single precision is the number which is encoded in 32 bits. Double precision floating point number is encoded with 64 bits. Table2 shows their properties.
Table 2: Floating point numbers
| Precision | Exponent | Mantissa | The smallest | The largest |
|---|---|---|---|---|
| Single (32 bit) | 8 bits | 23 bits | 10(-44.85) | 10(38.53) |
| Double (64 bit) | 11 bits | 52 bits | 10(-323.3) | 10(308.3) |
Data encoded in memory must be compatible with the processor. Memory chips are usually organised as a sequence of bytes, which means that every byte can be individually addressed. For processors of the class higher than 8-bit, there appears the issue of the byte order in bigger data types. There are two possibilities:
- Little Endian - low-order byte is stored at a lower address in the memory.
- Big Endian - high-order byte is stored at a lower address in the memory.
These two methods for a 32-bit class processor are shown in Fig1
