Computer Structure

Data Representing

• Original Code

  First digit represents symbol and the rest represent value.

    [+1]original = 0000 0001
      
    [-1]original = 1000 0001
      
  

• Inverse Code
  • Positive number: itself.
  • Negative number: the symbol bit remains unchanged, and the remaining bits are reversed.

    [+1] = [00000001]original = [00000001]反
      
    [-1] = [10000001]original = [11111110]反
  

• Complement
  • Positive number: itself.
  • Negative number: inverse code +1

    [+1] = [00000001]original = [00000001]反 = [00000001]补
      
    [-1] = [10000001]original = [11111110]反 = [11111111]补
      
    1+（-1) = 00000001 + 11111111 = 00000000 = 0
  

In a computer system, numeric values are always represented and stored by complements.

IEEE Standard 754 Floating Point Numbers

1. The Sign of Mantissa – 0 represents a positive number while 1 represents a negative number.
2. The Biased exponent –The exponent field needs to represent both positive and negative exponents.
3. The Normalised Mantissa –The mantissa is part of a number in scientific notation or a floating-point number, consisting of its significant digits. A normalised mantissa is one with only one 1 to the left of the decimal.

• Example

    85.125
    85 = 1010101
    0.125 = 001
    85.125 = 1010101.001
           =1.010101001 x 2^6
    sign = 0
      
    1. Single precision:
    biased exponent 127+6=133
    133 = 10000101
    Normalised mantisa = 010101001
    we will add 0's to complete the 23 bits
      
    The IEEE 754 Single precision is:
    = 0 10000101 01010100100000000000000
    This can be written in hexadecimal form 42AA4000
      
    2. Double precision:
    biased exponent 1023+6=1029
    1029 = 10000000101
    Normalised mantisa = 010101001
    we will add 0's to complete the 52 bits
      
    The IEEE 754 Double precision is:
    = 0 10000000101 0101010010000000000000000000000000000000000000000000
    This can be written in hexadecimal form 4055480000000000
  

• Zero – an exponent and mantissa of 0. -0 and +0 are distinct values, though they both are equal.
• Denormalised – this number does not have an assumed leading one before the binary point.
• Infinity – The sign bit distinguishes between negative infinity and positive infinity.
• Not A Number (NAN) – an error. This is a special value that might be used to denote a variable that doesn’t yet hold a value.

Little endian && Big endian

• Little endian: Low-byte data is stored at a low memory address, and high-byte data is stored at a high memory address.

• Big endian: High-byte data is stored at a low memory address, and low-byte data is stored at a high memory address.

  All network protocols use Big endian to transmit data.

Byte alignment

Improve the speed of access to data.

struct
{
    char a;
    short int b;
    int c;
    char d;
}