# Integer Numbers

#### Understanding Integer Numbers

• Integer numbers are a group of numbers that include all the whole numbers along with their negatives.
• They are represented on the number line where each integer has a distinct predecessor and successor.
• Difference between two integers is an integer.
• Product of two integers is also an integer.
• Note that integers include zero and negative values, unlike natural numbers.

#### Binary Representation of Integer Numbers

• Positive integer numbers are represented in the binary system similar to natural numbers.
• Dealing with negative integers in binary requires a system like two’s complement, which includes ‘flipping’ the bits and adding 1 to the binary representation.
• Understanding this binary representation of integers, both positive and negative, is crucial to understanding the fundamental operation of computers.

#### Encoding and Decoding Integer Numbers

• Encoding an integer number requires transforming a number from its original base (usually decimal) to another base, such as binary or hexadecimal.
• Different protocols might be deployed for positive and negative numbers, with Two’s Complement being common for negatives.
• Decoding follows the reverse process, where the integer is brought back to its original base from the encoded base representation.

#### Importance of Integer Numbers in Computing

• Integer numbers are used to represent quantities that may be increased or decreased, such as account balances or game scores.
• Specific instructions, called integer instructions, deal with integer data in machine-level operations.
• Understanding integers is crucial to understanding arithmetic underflows and overflows in computing.
• They also play a vital role in digital signal processing, graphics, and scientific computing.