# Computer Fundamentals Questions and Answers – The Hexadecimal Number System

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

7. Hexadecimal Addition of (3A5)16 and (1B2)16 will give :
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 to 2’s complement, we add 1 to the result. Remember that we should add 1 to the rightmost bit (LSB) even if it is a part of a fraction. So, 01.00+1=01.01.

9. Convert (6532)8 to hexadecimal.
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)
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?
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.

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