The smallest unit of Computer Memory: bit

  • Computers use memory devices built with electronics

  • The smallest memory device used by the computer works like a switch:

  • The smallest memory device can be in one of 2 states:

      • off state (which we call state 0)
      • on state (which we call state 1)   -- (0 and 1 are called binary digits)  

  • The smallest memory device is called a bit (= binary digit)

Building computer memory that can store larger numbers

  • A bit can be in one of 2 states:   0 or 1

    Therefore, a bit can store (= remember) one of 2 values:   0 or 1

  • A row of n bits can be in one of 2n states

    Each switch can be in 2 states.
    The total # combinations = 2 × 2 × ... × 2 = 2n

The binary number system

  • The binary number system uses 2 digits to represent/encode a number:

      • 0 = represents no value = (zero)
      • 1 = represents a unit value (= one)          

    This means that you can only use the digits 0 and 1 to write a binary number

  • Examples of binary numbers:

      • 10
      • 1010
      • 10101101
      • and so on.          

  • Question:   How do we assign a decimal value to a binary number ???

Value representation using the binary number system

  • The binary number system is a positional number system where value of digits increase by 2× for each digit position: 

                 1  0  1  0  1  0  0  1
             ^  ^  ^  ^  ^  ^  ^  ^
  Weight:    27  . . . . .  22 21 20
          = 128             4  2  1

    Examples: 

     Binary number:  1 0 1 0       Binary number:  1 1 0 1 1
 Weight:         8 4 2 1       Weight:        16 8 4 2 1
                ==========                   ===========
 Value:          8+0+2+0 = 10  Value:         16+8+0+2+1 = 27

Quiz: what is written on this T-shirt ?

  • What is the message on this T-shirt ?

  • Answer: ???

Quiz: what is written on this T-shirt ?

  • What is the message on this T-shirt ?

  • Answer: There are 2 (binary number 10) types of people in the world: ....

What does the binary number system has to do with computer memory ?

  • Recall that computer memory consists of memory cells:

  • Each memory cell is identified by a unique address (= a number)

  • Each memory cell stores a number

What does the binary number system has to do with computer memory ?

  • The computer uses the binary number system to represent the numbers:

  • Each memory cell is identified by a unique address as a binary number

  • Each memory cell stores a number as a binary number

Structure of the computer memory

  • In theory, we can make computer memory with any number of bits

  • For historical reasons, computer manufacturers have decided on memory cells that contains 8 bits:

  • We call a memory cell of 8 bits: one byte of memory

Computer memory jargon

  • A bit = a binary digit   --   which is the unit (= building block) of the computer memory

  • A byte = 8 bits   --   which is the unit of addressable/identfiable computer memory (you cannot use less than 1 byte in any computer operations)

  • KByte = kilo byte = 1024 (= 210) bytes (approximately 103 bytes)

  • MByte = mega byte = 1048576 (= 220) bytes (approximately 106 bytes)

  • GByte = giga byte = 1073741824 (= 230) bytes (approximately 109 bytes)
    *****   Today's computers has about 8-16 GBytes of RAM

  • TByte = tera byte = 1099511627776 (= 240) bytes (approximately 1012 bytes)
    *****   Today's hard disks can hold about 2-10 TBytes of data