This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Integers and Algorithms”.

1. The binary notation of 231 is

a) (11010111)_{2}

b) (10111011)_{2}

c) (11100011)_{2}

d) (11100111)_{2}

View Answer

Explanation: By binary Expansion of 11100111 is 1*2

^{0}+ 1*2

^{1}+ 1*2

^{2}+ 1*2

^{5}+ 1*2

^{6}+ 1*2

^{7}is equal to 231.

2. The decimal notation of 101010101 is

a) 340_{10}

b) 341_{10}

c) 342_{10}

d) 315_{10}

View Answer

Explanation: (101010101)

_{2}= 1*2

^{0}+1*2

^{2}+1*2

^{4}+1*2

^{6}+1*2

^{8}= 341.

3. The binary notation of ABBA is

a) 1010 1011 1011 1010

b) 1010 1001 1011 1011

c) 1011 1000 1010 1001

d) 1001 1000 1000 1111

View Answer

Explanation: By the base conversion algorithm.

4. The hexadecimal notation of (1011 0111 1011)_{2} is

a) (B2B)_{16}

b) (B5B)_{16}

c) (B7B)_{16}

d) (A7B)_{16}

View Answer

Explanation: (1011)

_{2}= 11 and (0111)

_{2}= 7, 11 in hexadecimal notation represents B. So it is (B7B)

_{16}.

5. The octal expansion of (10 1011 1011)_{2} is

a) (1245)_{8}

b) (1276)_{8}

c) (1275)_{8}

d) (1273)_{8}

View Answer

Explanation: (10 1011 1011)

_{2}= (699)

_{10}. Using base conversion algorithm, (699)

_{10}= (1273)

_{8}.

6. The hexadecimal expansion of (177130)_{10} is

a) (2B3EB)_{16}

b) (2B3EA)_{16}

c) (2C3AA)_{16}

d) (2B2AA)_{16}

View Answer

Explanation: Successively divide 177130 by 16 to obtain remainder they are (2B3EA)

_{16}.

7. The greatest common divisor of 414 and 662 is

a) 4

b) 5

c) 2

d) 6

View Answer

Explanation: By using Euclid Lemma.

8. The greatest common divisor of 12 and 18 is

a) 2

b) 3

c) 4

d) 6

View Answer

Explanation: By using Euclid Lemma, 6 divides 12 and 18.

9. The decimal expansion of (2AE0B)_{16} is

a) (175627)_{10}

b) (175624)_{10}

c) (178566)_{10}

d) (175622)_{10}

View Answer

Explanation: (2AE0B)

_{16}= 2*16

_{4}+10*16

_{3}+14*16

_{2}+0*16+11=(175627)

_{10}.

10. The greatest common divisor of 7 and 5 is

a) 1

b) 2

c) 5

d) 7

View Answer

Explanation: Two numbers 7 and 5 are relatively prime, so gcd(7, 5) = 1.

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