- The value of base in a decimal number system is __
a) 8
b) 2
c) 10
d) 16
Answer: (c) 10
Explanation: A decimal number system consists of 10 digits from 0 to 9. The definition of base describes it as a quantity to represent the number of digits present in that particular number system. Therefore, here, the base is 10.
2. Convert : (110)2 = ( __ )10 .
a) 4
b) 5
c) 6
d) 9
Answer: (c) 6
Explanation: The base 2 represents that the number is binary ,whereas, the base 10 represents that it is to be converted to the decimal format. Conversion: 22 * 1 + 21 * 1 + 20 *0 = 6.
3. The 2’s complement of 15 is __
a) 0000
b) 0001
c) 0010
d) 0100
Answer: (b) 0001
Explanation: 2’s complement is obtained by adding 1 to the 1’s complement of the number. Here, Binary of 15 = 1111 1’s complement of 15= 0000 2’s complement of 15= 0000+1=0001
4. Another name for base is __
a) root
b) radix
c) entity
d) median
Answer: (b) radix
Explanation: Another name for base is radix. Base refers to the number of digits that a particular number system consists of. The base of decimal number system is 10 , binary is 2 and so on.
5. The decimal equivalent of (0.101)2 will be __
a) 0.5
b) 0.625
c) 0.25
d) 0.875
Answer: (b) 0.625
Explanation: Since the base is 2 , it could be easily guessed that the number is binary. Conversion: 2-1 * 1 + 2-2 * 0 + 2-3 * 1 = 0.625.
6. The signed magnitude for -3 will be _
a) 00000011
b) 10000011
c) 11111101
d) 11111100
Answer: (b) 10000011
Explanation: Signed Magnitude of a number is a representation to determine if the number is positive or negative. If the MSB of a number is 0 , the number is positive , else if it is 1 the number is negative. Here, +3 = 00000011 -3= 100000011.
7. A number with both integer and a fractional part has digits raised to both positive and negative powers of 2 in a decimal number system.
a) True
b) False
Answer: (b) False
Explanation: In a decimal number system, a number with both integer and a fractional part has digits raised to both positive and negative powers of 10 and not 2. e.g. 22.34 = 2 * 101 + 2 * 100 + 3 * 10-1 + 4 * 10-2.
8. The hexadecimal representation of 14 is ___
a) A
b) F
c) D
d) E
Answer: (d) E
Explanation: The hexadecimal representations are as follows: 10 : A 11 : B 12 : C 13 : D 14 : E 15 : F.
9. Which of the following is not a decimal number?
a) 114
b) 43.47
c) 99.9A
d) 1010
Answer: (c) 99.9A
Explanation: All the numbers except 99.9A are decimal numbers. This number has a hexadecimal component A in it therefore, it is not a valid decimal number. The decimal equivalent of A is 10.
10. Select the incorrect option :
a) (101)10 = (1100101)2
b) G is valid in hexadecimal system.
c) C represents 12
d) The base of a decimal number system is 10
Answer: (b) G is valid in hexadecimal system.
Explanation: G is not a valid hexadecimal number. In this system , only representations from A to E are used to represent the numbers from 10 to 15. The base of the hexadecimal number system is 16
