Friday 25 January 2013

Introduction to Computing

Introduction to Computing


There are 3 kind of number systems.
  1. Base 10 (Decimal)- Human beings use. These are 0,1,2,3,...9
  2. Base 2 (Binary)- Computer use binary numbers. These are only 0 and 1, and these digits are commonly referred to as bits.
  3. Base 16 (Hexadecimal)-hexadecimal system,is used as a convenient representation of binary numbers.
It is much easier to represent a string of 0s and 1s such as 100010010110 as its hexadecimal equivalent of896H

  • The ASCII (pronounced “ask-E”) code assigns binary patterns for 
    • Numbers 0 to 9
    • All the letters of English alphabet,uppercase and lowercase
    • Many control codes and punctuation marks
    • The ASCII system uses 7 bits to represent each code

Conversion System:

Decimal to Binary conversiton

  • Divide the decimal number by 2 repeatedly
  • Keep track of the remainders
  • Continue this process until the quotient becomes zero
  • Write the remainders in reverse order to obtain the binary number

Binary to Decimal Conversion:

  • Know the weight of each bit in a binary number
  • Add them together to get its decimal equivalent

Decimal to Binary conversiton Through Weights


    • Use the concept of weight to convert a decimal number to a binary directly



    Represent a Binary in Hexadecimal Number

    • Start from the right and group 4 bits at a time, replacing each 4-bit binary number with its hex equivalent


    From Hex to Binary Conversion

    • Each hex digit is replaced with its 4-bit binary equivalent

    Decimal to Hex Conversion

    There are two methods to achieve this task.
    • Convert to binary first and then convert to hex
    • Convert directly from decimal to hex by repeated division, keeping track of the remainders

    Hex to Decimal Conversion

    There are Two Methods to achieve this.
    • Convert from hex to binary and then to decimal
    • Convert directly from hex to decimal by summing the weight of all digits



    Addition of two digits

    • Adding the digits together from the least significant digits
    • If the result is less than 16, write that digit as the sum for that position
    • If it is greater than 16, subtract 16 from it to get the digit and carry 1 to the next digit

    Subtraction

    • If the second digit is greater than the first, borrow 16 from the preceding digit






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