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Tuesday, 7 June 2016
ELECTRONICS SCIENCE CBSE NET EXAM SYLLABUS & PAPERS WITH ANSWER KEY(ONLY FOR M.SC STUDENTS)
https://drive.google.com/drive/folders/0Bws0-EJzLmKoRDhKck1xMEVOdVk
Saturday, 20 February 2016
Binary System Complement And Arithmatic
Binary system complements
Complements are used in the digital computers in order to simplify the subtraction operation and for the logical manipulations.
As the binary system has base r = 2. So the two types of
complements for the binary system are 2's complement and 1's complement.
1's complement
The 1's complement of a number is found by changing all 1's
to 0's and all 0's to 1's. This is called as taking complement or 1's
complement. Example of 1's Complement is as follows.
2's complement
The 2's complement of binary number is obtained by adding 1
to the Least Significant Bit (LSB) of 1's complement of the number.
2's complement = 1's complement + 1
Example of 2's Complement is as follows.
Binary arithmetic
Binary arithmetic is essential part of all the digital
computers and many other digital system.
1. Binary Addition
It is a key for binary subtraction, multiplication,
division. There are four rules of binary addition.
In fourth case, a binary addition is creating a sum of (1 +
1 = 10) i.e. 0 is written in the given column and a carry of 1 over to the next
column.
Example − Addition
2. Binary Subtraction
Subtraction and Borrow, these two words will be used very frequently for the
binary subtraction. There are four rules of binary subtraction.
Example − Subtraction
Shortcut methods For Number System Conversion
There Are many methods to convert number system to other number System here there are few shortcuts methods to covert one number system to another number system
- Binary to Octal
- Octal to Binary
- Binary to Hexadecimal
- Hexadecimal to Binary
1. Binary to Octal
Steps
- Divide the binary digits into groups of three (starting from the right).
- Convert each group of three binary digits to one octal digit.
Example
Binary Number 101012
Calculating Octal
Equivalent
Step
|
Binary Number
|
Octal Number
|
Step 1
|
101012
|
010 101
|
Step 2
|
101012
|
28 58
|
Step 3
|
101012
|
258
|
Binary Number 101012 = Octal
Number 258
2. Octal to Binary
Steps
- Convert each octal digit to a 3 digit binary number (the octal digits may be treated as decimal for this conversion).
- Combine all the resulting binary groups (of 3 digits each) into a single binary number.
Example
Octal Number 258
Calculating Binary
Equivalent
Step
|
Octal Number
|
Binary Number
|
Step 1
|
258
|
210 510
|
Step 2
|
258
|
0102 1012
|
Step 3
|
258
|
0101012
|
Octal Number 258 =
Binary Number 101012
3. Binary to
Hexadecimal
Steps
- Divide the binary digits into groups of four (starting from the right).
- Convert each group of four binary digits to one hexadecimal symbol.
Example
Binary Number 101012
Calculating hexadecimal
Equivalent
Step
|
Binary Number
|
Hexadecimal Number
|
Step 1
|
101012
|
0001 0101
|
Step 2
|
101012
|
110 510
|
Step 3
|
101012
|
1516
|
Binary Number 101012 =
Hexadecimal Number 1516
4. Hexadecimal to
Binary
Steps
- Convert each hexadecimal digit to a 4 digit binary number (the hexadecimal digits may be treated as decimal for this conversion).
- Combine all the resulting binary groups (of 4 digits each) into a single binary number.
Example
Hexadecimal Number − 1516
Calculating Binary
Equivalent −
Step
|
Hexadecimal Number
|
Binary Number
|
Step 1
|
1516
|
110 510
|
Step 2
|
1516
|
00012 01012
|
Step 3
|
1516
|
000101012
|
Hexadecimal Number 1516 =
Binary Number 101012
Number System Conversion
There are many methods
or techniques which can be used to convert numbers from one base to another.
We'll demonstrate here the following
- Decimal System to Binary System
- Binary System to Decimal System
- Octal System to Binary System
1. Decimal to Binary
System
Steps
- Divide the decimal number to be converted by the value of the new base.
- Get the remainder from Step 1 as the rightmost digit (least significant digit) of new base number.
- Divide the quotient of the previous divide by the new base.
- Record the remainder from Step 3 as the next digit (to the left) of the new base number.
Repeat Steps 3 and 4,
getting remainders from right to left, until the quotient becomes zero in Step
3.
The last remainder thus
obtained will be the Most Significant Digit (MSD) of the new base number.
Example :-
Decimal Number: 2910
Calculating Binary
Equivalent
Steps
|
Operation
|
Result
|
Remainder
|
Step 1
|
29 / 2
|
14
|
1
|
Step 2
|
14 / 2
|
7
|
0
|
Step 3
|
7 / 2
|
3
|
1
|
Step 4
|
3 / 2
|
1
|
1
|
Step 5
|
1 / 2
|
0
|
1
|
As mentioned in Steps 2
and 4, the remainders have to be arranged in the reverse order so that the
first remainder becomes the Least Significant Digit (LSD) and the last
remainder becomes the Most Significant Digit (MSD).
Decimal Number 2910 =
Binary Number 111012.
2. Binary System to
Decimal System
Steps
- Determine the column (positional) value of each digit (this depends on the position of the digit and the base of the number system).
- Multiply the obtained column values (in Step 1) by the digits in the corresponding columns.
- Sum the products calculated in Step 2. The total is the equivalent value in decimal.
Example :-
Binary Number : 111012
Calculating Decimal
Equivalent
Step
|
Binary Number
|
Decimal Number
|
Step 1
|
111012
|
((1 × 24) + (1 × 23) +
(1 × 22) + (0 × 21) + (1 × 20))10
|
Step 2
|
111012
|
(16 + 8 + 4 + 0 + 1)10
|
Step 3
|
111012
|
2910
|
Binary Number 111012 =
Decimal Number 2910
3. Octal System to Binary
System
Steps
- Convert the original number to a decimal number (base 10).
- Convert the decimal number so obtained to the new base number.
Example :
Octal Number − 258
Calculating Binary
Equivalent −
Step 1 − Convert to Decimal
Step
|
Octal Number
|
Decimal Number
|
Step 1
|
258
|
((2 × 81) + (5 × 80))10
|
Step 2
|
258
|
(16 + 5 )10
|
Step 3
|
258
|
2110
|
Octal Number 258 =
Decimal Number 2110
Step 2 – Convert Decimal to Binary
Step
|
Operation
|
Result
|
Remainder
|
Step 1
|
21 / 2
|
10
|
1
|
Step 2
|
10 / 2
|
5
|
0
|
Step 3
|
5 / 2
|
2
|
1
|
Step 4
|
2 / 2
|
1
|
0
|
Step 5
|
1 / 2
|
0
|
1
|
Decimal Number 2110 =
Binary Number 101012
Octal Number 258 =
Binary Number 101012
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