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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

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

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

Explanation: The hexadecimal number system comprises of only 15 symbols: 10 digits and 5 symbols. Hence, four bits (24 = 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

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

Explanation: To convert a hexadecimal number to decimal number:
161 * 5 + 160 * 2 = 80 + 2 = 82
Hence, the decimal equivalent is 82.

6. The hexadecimal equivalent of the binary number (0010010100)2 is :
a) (094)16
b) (0A4)16
c) 224
d) 0114

Explanation: To obtain the hexadecimal equivalent, we take numbers in groups of 4, from right to left as : 0000 1001 0100:
Here, 0000 = 0; 1001 = 9 and 0100 = 4
Therefore, the answer will be (094)16

a) 557
b) 185
c) 815
d) 516

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

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.

a) (A01)16
b) (A02)16
c) (D5A)16
d) (C01)16

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)

Therefore, the hexadecimal equivalent is (D5A)16.

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

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.

Sanfoundry Global Education & Learning Series – Computer Fundamentals.

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