Explain the concept of Number System- Binary , Decimal , Octal and Hexadecimal, conversion types, ASCII ,EBCDIC, EXCESS 3 Codes , Binary and Subtraction
1. BISHOP HEBER COLLEGE(AUTONOMOUS)
DEPARTMENT OF INFORMATION TECHNOLOGY
(Nationally Re-accredited with A Grade by NAAC with a CGPA
of 3.58 out of 4)
(Recognized by UGC as “College of Excellence”
Tiruchirappalli-620017,INDIA, www.bhc.edu.in
TEACHING LEARNING
Ms. G. VANITHA, MCA., M.Phil., B. Ed., NET,
Assistant Professor,
Department of Information Technology ,
Bishop Heber College, Tiruchirappalli-620-017
3. Number system
• Binary Number system-base value-2
• Octal Number system- Base value-8
• Decimal Number system-Base Value-10
• Hexadecimal Number system-16 (0-9,A,B,C,E, &
F)
11. BINARY to HEXADECIMAL
• Start from LSB, Each group of 4 bits replaced by its decimal equivalent.
• Ex
11110110101 = 0111 1011 01 01
7 B 5
12. Binary to decimal conversion
• Base value of binary =2
• Base value of decimal=10
13. Octal Number System
• Decimal to octal conversion base value or radix=8
• 8 ^0 =1 (0,1,2, … 7)
• Octal to decimal conversion
• Octal to binary conversion
• Binary to octal conversion
23. SIGNED & UNSIGNED
REPRESENTATION
(+) & (-) Sign before the number to represent its sign.
In computer is not possible. So 0 - positive number, 1- negative number.
For ex . + 15, - 15 are presented by 0 1111, 1 1111 respectively.
But negative numbers are represented in 3 ways
Signed –magnitude representation 1 1111
Signed -1’s complement representation 1 0000
Signed – 2’s complement representation 1 0001
24. FIXED-POINT REPRESENTATION OF
NUMBERS
• In the fixed point number representation systems,
• All numbers are represented as integers or fractions.
• Signed integer or BCD numbers are referred to as fixed-point
numbers.
• Ex.
• 123
25. FLOATING-POINT REPRESENTATION
OF NUMBERS
• A Number has both an integer part & a fractional part, is called a
real number or floating-point number., it can be either + or -.
• The numbers 0.008 & 1345.66 can be represented as 0.8X10 -2
&
1.34566X103
respectively.
• This kind of rep. is called the scientific representation.
• The number n can be represented as n=mr
e
, where m- mantissa, r-
radix & e- exponent.
26. BINARY CODED DECIMAL
• The BCD is the simplest binary code , i.e is used to represent a
decimal number..
• In BCD code 4 bit representation of a decimal number.
• Ex. 5 0101.
• If the decimal number consists of more than 1 digit , each decimal
digit is represented individually.
• Ex . 123 0001 0010 0011. 45 0100 0101
27. Gray code
• The gray code is binary code. It is used in shaft encoder.
• It is used in computer controlled machines such as lathes, etc.
28.
29. EXCESS- 3 CODE
• EXCESS-3 CODE is formed by adding 3 to the decimal number & then
forming the binary coded number.
• Ex. (435)10 to excess -3
4 3 5
3 3 3 Add
________
7 6 8 0111 0110 1000
________
31. ASCII code
• ASCII- American standard code for information
Interchange code.
• It a 7bit code, up to 128 characters .
• It is used in small computers, peripherals, instruments &
communication devices.
• A letter, digit or special symbol is called a character .
• 8th bit is parity , it may be 1 or 0.
32. ASCII-8 CODE
• A newer version of ASCII is the ASCII-8 code ,
• 8 bit code, up to 256 characters.
33. EBCDIC CODE
• EBCDIC stands for Extended BCD interchange code.
• It s a 8 bit code without parity.
• A 9th bit can be used for parity up to 256 characters.
• In ASCII -8 & EBCDIC , the 1st 4 bits are known as zone bit. And the
remaining 4 bits are digit values.
• ASCII 7 BIT 3,4
34. BITS,BYTES & WORDS
• A BYTE is a basic grouping of bits(binary digit)
• A word is a grouping of bits .
• 8 bit/16 bit /32 bit/64 bit word.
