Discrete Mathematics Multiple Choice Questions on “Integers and Algorithms”.
1. The binary notation of 231 is ___________
a) (11010111)2
b) (10111011)2
c) (11100011)2
d) (11100111)2
Answer: d
Clarification: By binary Expansion of 11100111 is 1*20 + 1*21 + 1*22 + 1*25 + 1*26 + 1*27 is equal to 231.
2. The decimal notation of 101010101 is ___________
a) 34010
b) 34110
c) 34210
d) 31510
Answer: b
Clarification: (101010101)2 = 1*20 + 1*22 + 1*24 + 1*26 + 1*28 = 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
Answer: a
Clarification: 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
Answer: c
Clarification: (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
Answer: d
Clarification: (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
Answer: b
Clarification: 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
Answer: c
Clarification: By using Euclid Lemma.
8. The greatest common divisor of 12 and 18 is?
a) 2
b) 3
c) 4
d) 6
Answer: d
Clarification: 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
Answer: a
Clarification: (2AE0B)16 = 2*164 + 10*163 + 14*162 + 0*16+11 = (175627)10.
10. The greatest common divisor of 7 and 5 is?
a) 1
b) 2
c) 5
d) 7
Answer: a
Clarification: Two numbers 7 and 5 are relatively prime, so gcd(7, 5) = 1.