## Computer Science Quiz - II: Part 2## Topic 5 - Digital Electronics1) Identify the Idempotent Law and Commutative Law - A * B = B * A and A * A = A
- A * A = A and A * B = B * A
- ~ (~ A) = A and A(B+C) = AB + AC
- None of these
Idempotent Law says operating the same operands gives the operand itself as a result. For Example: a + a = a and b . b = b If A * B = B * A then it is said to be commutative. 2) Which of the following claim is true about Ex-OR Gate? - Ex-OR satisfies Idempotent Law only
- Ex-OR satisfies Idempotent Law as well as Commutative Law
- Ex-OR satisfies both Commutative and Associative Law but not Idempotent Law
- Ex-OR satisfies both Idempotent and Associative law but not Commutative Law
a ⊕ a != a instead a ⊕ a = 0
a ⊕ b = b ⊕ a LHS = a ⊕ b = a' b + a b' = b' a + a' b = b ⊕ a (We know that OR (+) operation is commutative means a + b = b + a). Hence Proved.
a ⊕ ( b ⊕ c ) = ( a ⊕ b ) ⊕ c LHS = a ⊕ ( b ⊕ c ) = a ⊕ ( b' c + b c') = a' ( b' c + b . c') + a = a' b' c + a' b c' + a = a' b' c + a' b c' + a b' c' + a b c RHS = (a ⊕ b) ⊕ c = ( a' b + a b' ) ⊕ c = = = a' b' c + a b c + a' b c' + a b' c' = a' b' c + a' b c' + a b' c' + a b c = LHS Hence Proved. Therefore, (c) is the correct answer. 3) Which of the following claim is true about Ex-NOR Gate? - Ex-NOR satisfies Idempotent Law only
- Ex-NOR satisfies Idempotent Law as well as Commutative Law
- Ex-NOR satisfies both Commutative and Associative Law but not Idempotent Law
- Ex-NOR satisfies both Idempotent and Associative law but not Commutative Law
a ⊙ a != a instead a ⊙ a = 1
a ⊙ b = b ⊙ a LHS = a ⊙ b = a' b' + a b = b' a' + b a = b ⊙ a (We know that AND (.) operation is commutative means a . b = b . a). Hence Proved.
a ⊙ ( b ⊙ c ) = ( a ⊙ b ) ⊙ c LHS = a ⊙ ( b ⊙ c ) = a ⊙ ( b' c' + b c) = a' = a' = a' b' c + a' b c' + a b' c' + a b c RHS = ( a ⊙ b ) ⊙ c = ( a' b' + a b ) ⊙ c = = = a' b c' + a b' c' + a' b' c + a b c = a' b' c + a' b c' + a b' c' + a b c = LHS Hence Proved. Therefore, (c) is the correct answer. 4) How many different Boolean functions can be used with n Boolean variables at most? - 2 ^ n
^{2} - 2 ^ 2
^{n} - 2
^{n} - n
^{2}
5) How many different degree six Boolean functions exist? - 2
^{6} - 2
^{36} - 2
^{64} - 2
^{16}
Using formula: Number of Boolean functions = 2 ^ 2 = 2 ^ 2 = 2 ^ 64 Hence, (c) is the correct answer. 6) A Boolean expression's dual is produced by swapping - Boolean Sums and Boolean Products or interchanging 0s and 1s
- Boolean Products and Boolean sums and interchanging 1s and 0s
- Boolean Products and Boolean Sums
- Interchanging 0s and 1s
If we take a function f (a, b, c, d, ......, z, 0, 1, +, .) as an example, its dual is defined as fd (a, b, c, ......, z, 0, 1, ., +). Dual functions are referred to when the nature of the variable does not change but 0 ? 1, 1 ? 0, or ? and, and ? or. When we take the dual of a function, its functionality is preserved, but a positive logic system is changed into a negative logic system because a function is independent of magnitude, if it functions correctly in a positive logic system, it must likewise function correctly in a negative logic system. 7) Select the correct option The dual of x + y z is - x' + y' z'
- x' . ( y' + z' )
- x . ( y + z )
- x + y z
8) A Boolean function's dual, denoted by the symbol F - 2n
- 2n-1
- 2^2
^{n} - 2^2
^{n-1}
For n variable functions, a total of 2 9) Using Boolean algebra, the absorption law states that - a + a' . b = a + b
- a . a = a
- a + a . b = a
- None of the above
LHS = a + a . b = a . ( 1 + b ) = a . 1 = a Hence Proved. 10) Using Boolean algebra, the compensation theorem states that - a + a' . b = a + b
- a . a = a
- a + a . b = a
- None of the above
Here, a represents minterm number 2 and 3 and a' b represents minterm number 1. So, we have obtained two groups of the minterm. To represent minterm number 2 and 3, we have a and to represent minterm number 1 and 3, we have b. The minimized equation is a + b = RHS. Hence proved. 11) Take into account the four-variable Boolean function that follows: F ( w, x, y, z) = ? ( 1, 3, 4, 6, 9, 11, 12, 14) What is the simplest version of the function that the Karnaugh map may represent? - x' z + x z'
- x' z' + x z
- w' x + y' z
- w y + z y
Using K-map, we have Image Here: There are two groups of minterms: ? ( 4, 6, 12, 14) can be represented by x z', ? ( 1, 3, 9, 11) can be represented by x' z. The minimized function is x z' + x' z. Therefore, (a) is the correct answer. 12) Which is an example of universal gate? - Ex-OR gate
- Ex-NOR gate
- ANS gate
- NOR gate
13) Logic gates can be used to implement an equation for the sum of products. - AND - OR
- NAND - OR
- AND - NOT
- OR - AND
It is a two-level implementation. In the first level, we use AND gates to find the product terms of the Boolean equation and in the second level, we use OR gate to sum those product terms. Eventually, we get the equation in the form of SOP (sum of products.) Image Here 14) How many NAND gates must be used as a minimum to build a 2-input EXCLUSIVE-OR function without the aid of any other logic gates? - 2
- 3
- 4
- 5
Image Here 15) Select the correct option - Half adder is Ex-OR and AND Circuit
- Half adder is Ex-NOR and AND Circuit
- Half adder is NAND and NOR Circuit
- Half Adder is AND and OR Circuit
Half-adders are combinational circuits that execute the arithmetic addition of two one-bit binary values. Therefore, two single binary bits A and B are added in half adders, and two outputs, sum (S) and carry (c), are produced. It is implemented using Ex-OR and AND gates. Ex-OR determines the SUM and AND determines the Carry as shown below: Image Here 16) Which of the subsequent statements is accurate? I. A half adder is a circuit that adds two bits to produce a sum bit and a carry bit. II. A full adder is a circuit that adds two bits to produce a sum bit and a carry bit. III. A circuit known as a full adder produces a sum bit and a carry bit by adding two bits and a carry bit. IV. An inverter is a piece of equipment that takes the value of a Boolean variable as input and outputs its complement. - I, II, and IV only
- III and IV only
- I and II only
- I, III, and IV only
SUM = A Where C
Therefore, option I, III, and IV are true and II is false. Hence, (d) is the correct answer. 17) Consider the following input values for a full - adder: I. x = 0, y = 1 and C II. x = 1, y = 0 and C For the aforementioned input numbers, calculate the values of S (sum) and C - S = 1, C
_{o}= 0 and S = 0, C_{o}= 1 - S = 0, C
_{o}= 1 and S = 1, C_{o}= 0 - S = 0, C
_{o}= 0 and S = 1, C_{o}= 1 - S = 1, C
_{o}= 0 and S = 1, C_{o}= 0
For a full adder: Sum = A ⊕ B ⊕ C, and Carry = A . B + B . C + A . C
Sum = 0 ⊕ 1 ⊕ 1 = 0 Carry =0 . 1 + 1 . 1 + 0 . 1 = 0 + 1 + 0 = 1
Sum = 1 ⊕ 0 ⊕ 0 = 1 Carry = 1 . 0 + 0 . 0 + 1 . 0 = 0 + 0 + 0 = 0 Hence, (b) is the correct answer. 18) A logic circuit that __________ is a multiplexer. - requires one input to produce several outputs
- has several inputs and outputs
- accepts numerous inputs and produces just one output
- requires one input and produces one output
A unique and popular type of combinational circuit is the multiplexer. The primary criterion is that we must choose one input from a large number of inputs, such as a telephone call or a train departing the station. Using a combinational circuit known as a multiplexer, binary data is chosen from one or more input lines and sent to a single output line. A group of selection lines regulates the choice of a specific input line. There are n selection lines and 2n input lines, and the bit combinations on the selection lines determine which input is chosen. Since it chooses one of the numerous inputs and directs the binary data to the output line, a multiplexer is also known as a data selector. Image Here Hence, (c) is the correct answer. 19) If both the S and R inputs of an SR latch created by cross-coupling two NAND gates are set to 0, the following will be the result: - Q = 0 and Q' = 1
- Q = 1 and Q' = 0
- Q = 1 and Q' = 1
- Indeterminate state
Image Here
We shall obtain both Q and Q' as 1 when R and S are set to 0. This output will last forever and does not depend on the inputs and not on the sequence in which events occur. The output leads to an uncertain state. However, if R = S = 1 is set after this state, the circuit will act like a buffer, and Q will remain Q. (Either Q = 0, and Q' = 1 or Q = 1 and Q' = 0). Thus, the correct answer is both (c) and (d). 20) Think of a 4-bit Johnson counter with the value 0000 as its starting point. This counter's counting pattern is - 0, 1, 3, 7, 15, 14, 12, 8, 0
- 0, 1, 3, 5, 7, 9, 11, 13, 15, 0
- 0, 2, 4, 6, 8, 10, 12, 14, 0
- 0, 8, 12, 14, 15, 7, 3, 1, 0
This is how it will operate: 0000 = 0 1000 = 8 1100 = 12 1110 = 14 1111 = 15 0111 = 7 0011 = 3 0001 = 1 0000 = 0 Therefore (d) is the correct answer. Next TopicWhat is a Palmtop Computer? |