Representing unsigned (integer) values inside the computer
 

 

  • Computers use the binary number system to represent (= store) unsigned (integer = whole) numbers.

  • The binary number system is similar to the decimal number system that you have learned in high school

The binary number system (repeat + summary)

The binary number system:

Storing integer (whole) values inside a computer program
 

Storing integer (whole) values:

  • Computer memory was a scarce resource (used to be very expensive !)

  • Traditionally, programming language provided integer representations of different lengths for different needs

    • Shorter representations to minimize storage requirements

    • Longer representations to maximize accuracy requirements

Storing integer (whole) values inside a computer program
 

Program data types to represent (store) integer (whole) values:

  • byte: uses 1 byte of memory

  • short: uses 2 bytes of memory

  • int: uses 4 bytes of memory

  • long: uses 8 bytes of memory

Storing integer (whole) values inside a computer program

How to store (= represent) the value 5 in different data types:

Interpreting binary numbers

 

Converting from binary ⇒ decimal representation
 

Converting from decimal ⇒ binary representation
 

 

Example:

     • Find the 8 bits binary representation for the decimal representation 89
       (I'll work it out in class)

Converting from decimal ⇒ binary representation

Solution:

Quiz 1 - Applying what you have learned

 

Quiz 1 - Applying what you have learned

 

Answer: 

       9 decimal    ⇒  1001  binary          

       Stored in 1 byte:    00001001

       Therefore, x contains:   00001001

Quiz 2 - Applying what you have learned

 

Quiz 2 - Applying what you have learned

 

Answer: 

 9 decimal    ⇒  1001  binary 

 Stored in 4 bytes:   00000000 00000000 00000000 0001001 

 Therefore, x contains: 00000000000000000000000000001001

A "binary number" joke...