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?
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.
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:
Explanation: The hexadecimal number system comprises of only 15 symbols: 10 digits and 5 symbols. Hence, three bits (24 = 16 ) are sufficient to represent any hexadecimal number in the binary format.
4. The binary number 1110 in hexadecimal format is _____________
Explanation: Certain binary to hexadecimal representations are :
5. Convert (52)16 into its decimal equivalent.
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 :
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 :
Explanation: Octal subtraction is done as follows:
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.
8. The 2’s complement of 10.11 :
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.
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?
b) hexadecimal point
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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