CS2.201 - Computer Systems Organization | CSO Lecture 3 Notes

Storage Format

• Big Endian: The data inside a word is stored in left to right format, or most significant byte is stored leftmost.

  | 01 | 23 | 45 | 67 |
  

• Little Endian: The data inside a word is stored in right to left format, or least significant byte is stored leftmost.

  | 67 | 45 | 23 | 01 |
  

Bitwise operations in C

Integer ranges

Unsigned Integers

We take the decimal representation of a $w$ length bit string as $\sum_{i = 0}^{w - 1} x_i 2^i$

Signed Integers

We take the decimal representation of a $w$ length bit string as $(-1)^{x_{w - 1}} \sum_{i = 0}^{w - 2} x_i 2^i$

However, this would mean we have two zeros, eg. in 4 bits, $(1000)_2$ and $(0000)_2$

In order to solve this problem, we use two’s compliment representation

Signed Integers - Two’s Complement Representation

$-(x_{w-1} 2^{w-1}) + \sum_{i = 0}^{w - 2} x_i 2^i$

Isomorphism between binary, unsigned and two’s complement integer arithmetic (modular)

The same bitstring can have a different numerical value depending on which system it is interpreted in, unsigned or two’s complement.

Copying to an extended size datatype

If we want to copy a 4 bit unsigned integer to an 8 bit type, we can just pad the 8 bit with 4 zero bits, and then the original 4 bit number.

For two’s complement, if we have a positive number we do the same, but if we have a negative number, we have to pad the 8 bit with 4 one bits, and then the original 4 bit number.

For eg:

0011 -> 00000011 : signed or unsigned
1011 -> 11111011 : signed