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Data Representation (Number Systems :1234: (Binary:Base:2 Elements (0,1),…
Data Representation
Numeric
: contain Real (Number with decimal point) and Integers (Number without decimal point)
Alphabetic
: contain alphabets
Alpha Numeric
: contains alphabets,number and special symbols. also called a character (8 bit size)
Number Systems :1234:
Binary
:Base:2 Elements (0,1)
Decimal
:Base:10 Elements(0,1,2,3,4,5,6,7,8,9)
Octal
:Base:8 Elements(0,1,2,3,4,5,6,7)
HexaDecimal
:Base:16 Elements(0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F)
Number System Conversions
Binary
Binary to Decimal:
(1)
Raise doubled powers from right hand side and add powers of 1s only.
(2)
Multiply each digit with 2 and raise increasing power (start from 0) from right hand side, then add all results.
Binary to Octal:
Make group of 3 digits and raise doubled powers from right hand side, then add powers on 1s.
Binary to HexaDecimal:
Make group of 4 digits and raise doubled powers from right hand side, then add powers on 1s.
Decimal
Decimal to Binary
Find LCM with 2. Take remainders from bottom to top and Place them in left to right order.
Decimal to Octal
Find LCM with 8. Take remainders from bottom to top and Place them in left to right order.
Decimal to HexaDecimal
Find LCM with 16. Take remainder from bottom to top and Place them in left to right order.
Octal
Octal to Decimal:
Multiply each digit with 8 and raise increasing power (start from 0) from right hand side, then add all results.
Octal to Binary:
Convert each digit into 3 bit binary
Octal to HexaDecimal
Convert each digit into 3 bit binary. Write all binary digits together. Make group of 4 digits and raise doubled powers from right hand side, then add powers on 1s.
HexaDecimal
HexaDecimal to Decimal
: Multiply each digit with 16 and raise increasing power (start from 0) from right hand side, then add all results.
HexaDecimal to Binary
: Convert each digit into 4 bit binary
HexaDecimal to Octal
Convert each digit into 4 bit binary. Write all binary digits together. Make group of 3 digits and raise doubled powers from right hand side, then add powers on 1s.
Coding Schemes
Binary Coded Decimal(BCD):
A 4 bit coding scheme to represent a decimal number into binary.
ASCII Codes:
Stands for American Standard Code for Information Interchange. A 7 bit coding scheme for representing characters