This set of Tough Computer Fundamentals Questions and Answers focuses on “The Hexadecimal Number System”.

1. What does the symbol D represent in a hexadecimal number system?

a) 8

b) 16

c) 13

d) 14

View Answer

Explanation: The symbols A, B, C, D, E and F represent 10, 11, 12, 13, 14 and 15 respectively in a hexadecimal system. This system comprises of 15 numbers in total: digits from 0-9 and symbols from A to F.

2. ABC is a valid hexadecimal number.

a) True

b) False

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Explanation: In a hexadecimal number system, alphabets are used for the representation of numbers from 10 to 15. Here, A represents 10, B represents 11 and C represents 12. Therefore, it is a valid hexadecimal number.

3. The maximum number of bits sufficient to represent a hexadecimal number in binary:

a) 4

b) 3

c) 7

d) 8

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Explanation: The hexadecimal number system comprises of only 15 symbols: 10 digits and 5 symbols. Hence, three bits (2

^{4}= 16 ) are sufficient to represent any hexadecimal number in the binary format.

4. The binary number 1110 in hexadecimal format is _____________

a) 6

b) E

c) 14

d) 15

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Explanation: Certain binary to hexadecimal representations are :

1010=A

1011=B

1100=C

1101=D

1110=E

1111=F.

5. Convert (52)_{16} into its decimal equivalent.

a) 28

b) 83

c) 80

d) 82

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Explanation: To convert a hexadecimal number to decimal number:

16

^{1}* 5 + 16

^{0}* 2 = 80 + 2 = 82

Hence, the decimal equivalent is 82.

6. The hexadecimal equivalent of the binary number (0010010100)_{2} is :

a) 0B4

b) 0A4

c) 224

d) 0114

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Explanation: To obtain the octal equivalent, we take numbers in groups of 3, from right to left as :

7. Hexadecimal Addition of (3A5)_{16} and (1B2)_{16} will give :

a) 165

b) 185

c) 815

d) 516

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Explanation: Octal subtraction is done as follows:

3A5

+ 1B2

________

557

In hexadecimal addition of alphabets, we add the corresponding numbers they represent and then subtract the result from 16, then generate a carry of 1 to the next set of numbers.

Here, 5+2=7

A+B=10+11=21-16=5

3+1+1(carry)=5.

8. The 2’s complement of 10.11 :

a) 10

b) 0.010

c) 01.01

d) 10.01

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Explanation: The 1’s complement of a number is obtained by reversing the bits with value 1 to 0 and the bits with value 0 to 1. Here, 10.11 gets converted to 01.00 in its 1’s complement format. Further, to convert 1’s complement into 2’s, we add 1 to the result. Here, 01.00+1=10.00.

9. Convert (6532)_{8} to hexadecimal.

a) A01

b) A02

c) B01

d) C01

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Explanation: To convert octal to hexadecimal, we first write binary format of the number and then make groups of 4 bits from right to left, as follows:

6 5 3 2 110 101 011 010 (octal -> binary) 1101 0101 1010 ( groups of 4) D 5 A ( hexadecimal equivalent)

Therefore, the hexadecimal equivalent is (D5A)_{16}.

10. What do we call the point(decimal) in any hexadecimal number of the form 111.A3?

a) radix

b) hexadecimal point

c) decimal

d) octal point

View Answer

Explanation: The decimal is often referred to as the hexadecimal point in hexadecimal representation of numbers.

It is referred to as the octal point in octal numbers.

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