ICT Lecture 7:
Number System
So, the binary number for given decimal is: (10100)2
Number System
Number system is a way to represent a set of values in different quantities.
Common number systems are:
Ø Binary Number System (Base 2)
Ø Octal Number System (Base 8)
Ø Decimal Number System (Base 10)
Ø Hexadecimal Number System (Base 16)
Note: If base (or radix) of any number is ‘r’, then digits allowed in that number system is ‘r-1’. For example, decimal number has base(r) =10, thus any number in decimal is combination of 0 to 9 (i.e. 0 to r-1).
Binary Number System- Binary number system consists of two digits 0 and 1. The base of number is 2. Any number can be represented with combinations of 0s and 1s. The computer system understands machine language which is in form of 0s and 1s. Thus, machine language is also known as binary language.
For example:
Binary number is written as: (1011)2
Octal Number System- Octal number system consists of eight digits 0 and 7. The base of number is 8. Any number can be represented with combinations of 0 to 7 digits.
For example:
Octal number is written as: (1206)8
(6785)8 is not valid octal number because octal number can have digits from 0 to 7.
Decimal Number System- This is the number system that we use in our day to day life. Decimal number system consists of ten digits 0 and 9. The base of number is 10. Any number can be represented with combinations of 0 to 9 digits.
For example:
Decimal number is written as: (1206)10
Hexadecimal Number System- Hexadecimal number system consists of eight digits 0-9, A-F. The base of number is 16. Any number can be represented with combinations of 0 to 9 digits, A-F alphabets.
For example:
Hexadecimal number is written as: (A6)16
Hexadecimal number system consists of 0-9, A-F. Here, A=10, B=11, C=12, D=13, E=14 and F=15.
Number System
|
Base/Radix
|
Digits used
|
Binary
|
2
|
0-1
|
Octal
|
8
|
0-7
|
Decimal
|
10
|
0-9
|
Hexadecimal
|
16
|
0-9, A-F
|
Decimal to Binary Conversion:
For converting a decimal number to binary we have two methods.
Method 1:
Divide the given decimal number by 2 and note down remainder. Then, read these remainders from bottom to top.
For example, (20)10= (?)2
So, the binary number for given decimal is: (10100)2
Method 2:
The binary number is always in the form of 2x . So, it can be represented by combination of 20, 21, 22, 23, 24,25………. (in reverse).
For example, (20)10= (?)2
24
|
23
|
22
|
21
|
20
|
16
|
8
|
4
|
2
|
1
|
1
|
0
|
1
|
0
|
0
|
20 can be represented as sum of (16+4).
Thus, write '1' at the place of 16 and 4 and '0' at other places.
So, the binary number for given decimal is: (10100)2
UGC NET Previous Years Questions
1. Which number system is usually followed in a typical 32-bit computer? (June 2010)
(A) 2
(B) 8
(C) 10
(D) 16
Answer: (A)
2. Which one of the following represents the binary equivalent of the decimal number 23? (June 2010)
(A) 01011
(B) 10111
(C) 10011
(D) None of the above
Answer: (B)
Description:
(A) 0 – 7
(B) 0 – 9 , A – F
(C) 0 – 7, A – F
(D) None of these
Answer: (B)
4. The octal number system consists of the following symbols: (June 2011)
(A) 0 – 7
(B) 0 – 9
(C) 0 – 9, A – F
(D) None of the above
Answer: (A)
5. Which one of the following is correct? (Dec 2012)
(A) (17)10 = (17)16
(B) (17)10 = (17)8
(C) (17)10 = (10111)2
(D) (17)10 = (10001)2
Answer: (D)
Description: Using Method 2: (16+1=17)
24
|
23
|
22
|
21
|
20
|
16
|
8
|
4
|
2
|
1
|
1
|
0
|
0
|
0
|
1
|
6. Binary equivalent of decimal number 35 is (Dec 2014)
(A) 100011
(B) 110001
(C) 110101
(D) 101011
Answer: (A)
7. Symbols A-F are used in which one of the following? (Dec 2014)
(A) Binary number system
(B) Decimal number system
(D) Octal number system
Answer: (C)
8. Which one of the following represents the binary equivalent of the decimal number 25? (June 2015)
(A) 11011
(B) 10101
(C) 01101
(D) 11001
Answer: (D)
9. The binary equivalent of the decimal number 48 is 110000, then the binary equivalent of the decimal number 51 is given by (July 2016)
(1) 110011
(2) 110010
(3) 110001
(4) 110100
Answer: (1)
(2) 110010
(3) 110001
(4) 110100
Answer: (1)
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