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