Computer fundamentals

Computer fundamentals
Data Representation in Computers

Objectives
Introduction (Bit, Byte, KB, MB, GB)
The Decimal Number System
The Binary Number System
Number Conversion between Number Systems
Data Storage
Binary Arithmetic
Unit of Information
Data Representation
Data is stored in a computer in binary format as a series of 1s and 0s.
Computers use standardized coding systems (such as ASCII) to determine what character or number is represented by what series of binary digits.
Data is stored in a series of 8-bit combinations called a byte.
Every letter, number, punctuation mark, or symbol has its own unique combination of ones and zeros.
Data Representation
On
Off
A bit or binary digit has one of two values, zero or one
A byte is the smallest addressable unit of memory (8 bits)
ASCII provides for 256
(or 28) characters
01000001 – A
01000010 – B
etc.

Memory Bits and Bytes
8 Bits = 1 Byte
Memory Bits and Bytes
Bits are switches turned ‘on’ or ‘off’



ON bits are said to be in a 1 state
OFF bits are said to be in a 0 state


Memory Bits and Bytes
ON bits are said to be in a 1 state
OFF bits are said to be in a 0 state


0
0
0
1
1
1
0
0
Combination of 1’s and 0’s represent the letters, numbers, and special characters.
Allows for 256 combinations.
Bits and Bytes


8 bits = 1 Byte (1 keyboard character)
1,024 bytes = 1 Kilobyte (1K)
1,024 K = 1 Megabyte (MB)
1,024 MB = 1 Gigabyte (GB)
Memory
Transient (erased when power turned off)
Consider a UPS (uninterrupted power supply)
Measured in bytes
1 Kilobyte = 210 characters (~1,000 bytes)
1 Megabyte = 220 characters (~1,000,000 bytes)
1 Gigabyte = 230 characters (~1,000,000,000 bytes)
Need 256Mb or 512Mb of RAM
Keep multiple programs & data files in memory
Graphic-intensive programs demand a lot of memory
The Original PC had 16Kb of memory
The Decimal Number System
In the decimal system use from 0 to 9
We consider the number: 365
(3x100) + (6x10) + (5x1) = 365
(3x102) + (6x101) + (5x100) = 365
Thus as we move one position to the left, the value of the digit increases by ten times
The value of each digit in the number system is determined by:
- The digit itself
- The position of the digit in the number itself
- The base/radix of the system
The Binary Number System
The binary number system has a base of two, and symbols used are 0 and 1.
Example: 1010
(1x8) + (0x4) + (1x2) + (0x1) = 1010
(1x23) + (0x22) + (1x21) + (0x20) = 1010
Thus as we move to the left the value of the digit will be two times greater than its predeccessor.
The value of the places are:
  64  32  16  8  4  2  1
Converting Binary to Decimal
The decimal equivalent of 110100 is
(1x32) + (1x16) + (0x8) + (1x4) + (0x2) + (0x1)
= 32 + 16 + 0 + 4 + 0 + 0
= 52
Converting Decimal To Binary
In conversion from decimal to any other number system, the steps to be followed are:
- Divide the decimal number by the base of the requred number system
- Note the remainder in one column and divide the qoutient again with the base. Keep repeating this process until the quotient is reduced to a zero
- Reading off the remainder in the reverse order of them being written down will give us the required number.
Converting Decimal To Binary
Example: Convert the decimal number 52 to its binary equivalent
Thus the binary equivalent of the decimal number 52 is 110100