# Discrete Mathematics Questions and Answers – Logic and Bit Operations

This set of Discrete Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Logic and Bit Operations”.

1. Which of the following bits is the negation of the bits “010110”?
a) 111001
b) 001001
c) 101001
d) 111111

Explanation: Flip each of the bit to get the negation of the required string.

2. Which of the following option is suitable, if A is “10110110”, B is”11100000” and C is”10100000”?
a) C=A or B
b) C=~A
c) C=~B
d) C=A and B

Explanation: Output of and is 1 when both other inputs are one.

3. How many bits string of length 4 are possible such that they contain 2 ones and 2 zeroes?
a) 4
b) 2
c) 5
d) 6

Explanation: The strings are {0011, 0110, 1001, 1100, 1010 and 0101}.

4. If a bit string contains {0, 1} only, having length 5 has no more than 2 ones in it. Then how many such bit strings are possible?
a) 14
b) 12
c) 15
d) 16

Explanation: The total strings are 1(having no one in it) +5(having 1 one in it) +10 (having 2 ones in it) = 16.

5. If A is “001100” and B is “010101” then what is the value of A (Ex-or) B?
a) 000000
b) 111111
c) 001101
d) 011001

Explanation: In Ex-or if both the inputs are same then output is 0 otherwise 1.

6. The Ex-nor of this string “01010101” with “11111111” is?
a) 10101010
b) 00110100
c) 01010101
d) 10101001

Explanation: In Ex-nor if both the inputs are same then output is 1 otherwise 0.
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7. What is the one’s complement of this string “01010100”?
a) 10101010
b) 00110101
c) 10101011
d) 10101001

Explanation: Negate every bit in one’s complement.

8. What is the 2’s complement of this string “01010100”?
a) 10101010
b) 00110100
c) 10101100
d) 10101001

Explanation: In two’s complement negate every bit from left until the first one from right is encountered.

9. If in a bits string of {0,1}, of length 4, such that no two ones are together. Then the total number of such possible strings are?
a) 1
b) 5
c) 7
d) 4

Explanation: Strings can be {1001, 1010, 0101, 1000, 0100, 0010, 0001}.

10. Let A: “010101”, B=?, If { A (Ex-or) B } is a resultant string of all ones then which of the following statement regarding B is correct?
a) B is negation of A
b) B is 101010
c) {A (and) B} is a resultant string having all zeroes
d) All of the mentioned

Explanation: In Ex-or both if both the inputs are the same then output is 0 otherwise 1.

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