Binary Number Encoding and Arithmetic

Digit Information Encodeing

1. Using discrete symbols or digits
2. These are typical binary digits(bits):0 and 1
   
3. we can implement operations like +,>,AND,etc. on binary numbers in hardware very effiently

Encoding Positive Integers

questions:

1. how to encoding integers by binary system
2. how to represent numbers by hexadecimal
3. how do Binary Addition and Binary Subtraction work
4. what is “overflow”
5. what is modular arithmetic

Encoding Negative Integers

questions:

1. how to encode using a sign-magnitude representation
2. what issues might this encoding have

Two’s complement Encoding

We can simply relabel some of the digits to represent negative numbers while retaining the nice properties of modular arithmatic

In two’s complement encoding,the high-order of the N-bit representation has nagetive weight:

negative number has “1” in the high-order bit

Arithmetic

negate

invert all the bits and add one

substract

negate the subtrahend and add to the minuend

Example:

Summary