# Discrete Mathematics Questions and Answers – Number Theory – Base Conversion

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This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Number Theory – Base Conversion”.

1. Which of the number is not allowed in Binary representation of a number?
a) 0
b) 1
c) 2
d) None of the mentioned

Explanation: Binary numbers are formed with a combination of 0 & 1 only.

2. Which of the number is not allowed in Octal representation of a number?
a) 0
b) 4
c) 8
d) None of the mentioned

Explanation: Octal numbers are formed with a combination of 0 to 7 only.

3. Hexadecimal number equivalent of decimal 10 is?
a) 10
b) A
c) F
d) None of the mentioned

Explanation: In hexadecimal representation A is represented as decimal 10.

4. Decimal equivalent of binary number 1010 is?
a) 11
b) A
c) 10
d) None of the mentioned

Explanation: 0X1 + 1X2 + 0X4 + 1X8 = 10 in decimal.

5. Decimal 13 in base 8 can be represented as _________
a) 15
b) 12
c) 22
d) None of the mentioned

Explanation: 1X8 + 5X1 = 12, 15 is the octal representation of 13.

6. F in hexadecimal representation is equivalent to 9 in decimal.
a) True
b) False

Explanation: F in hexadecimal representation is equivalent to 15 in decimal.

7. Octal number may contain digits from 1 to 8.
a) True
b) False

Explanation: Octal number contains digits from 0 to 7, * is not allowed.

8. For some base r, the digits which are allowed in its representation are?
a) Digits from 1 to r
b) Digits from 0 to r-1
c) Digits from 1 to r-1
d) None of the mentioned

Explanation: A base r number may contain digits from 0 to r-1.

9. The binary number 100110 in octal is represented by _______________
a) 45
b) 10012
c) 46
d) 58

Explanation: Pairing 3 numbers from right hand side we get 110 as 6 and 100 as 4 in octal so the number is 46.

10. A number greater than 32 would require a minimum of how may bits in binary representation?
a) 5
b) 6
c) 4
d) 10 