# Consider three 4-variable functions f1, f2, and f3, which are expressed in sum-of-min terms asf1 = ∑ (0, 2, 5, 8, 14), f2 = ∑ (2, 3, 6, 8, 14, 15), f3 = ∑ (2, 7, 11, 14)For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

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## Options:

1. ∑ (7, 8, 11)

2. ∑ (2, 7, 8, 11, 14)

3. ∑ (2, 14)

4. ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)

### Correct Answer: Option 1 (Solution Below)

This question was previously asked in

GATE CS 2019 Official Paper

## Solution:

Let X = f1.f2

= (0, 2, 5, 8, 14).(2, 3, 6, 8, 14, 15)

= (2, 8, 14)

X ⊕ f3

= (2, 8, 14) ⊕ (2, 7, 11, 14)

= (2, 8, 14).(2, 7, 11, 14)’ + (2, 8, 14)’.(2, 7, 11, 14)

= (2, 8, 14).(0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15) + (0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15).(2, 7, 11, 14)

= (8) + (7, 11)

=(7, 8, 11)

(f1.f2) ⊕ f3 = ∑ (7, 8, 11)
The text contains a mathematical question related to digital logic and Boolean algebra, specifically about finding the output function of a circuit with given input functions. The solution to the problem is provided in the text.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Consider three 4-variable functions f1, f2, and f3, which are expressed in sum-of-min terms asf1 = ∑ (0, 2, 5, 8, 14), f2 = ∑ (2, 3, 6, 8, 14, 15), f3 = ∑ (2, 7, 11, 14)For the following circuit with one AND gate and one XOR gate, the output function f can be expressed as:

Free Practice With Testbook Mock Tests

## Options:

1. ∑ (7, 8, 11)

2. ∑ (2, 7, 8, 11, 14)

3. ∑ (2, 14)

4. ∑ (0, 2, 3, 5, 6, 7, 8, 11, 14, 15)

### Correct Answer: Option 1 (Solution Below)

This question was previously asked in

GATE CS 2019 Official Paper

## Solution:

Let X = f1.f2

= (0, 2, 5, 8, 14).(2, 3, 6, 8, 14, 15)

= (2, 8, 14)

X ⊕ f3

= (2, 8, 14) ⊕ (2, 7, 11, 14)

= (2, 8, 14).(2, 7, 11, 14)’ + (2, 8, 14)’.(2, 7, 11, 14)

= (2, 8, 14).(0, 1, 3, 4, 5, 6, 8, 9, 10, 12, 13, 15) + (0, 1, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 15).(2, 7, 11, 14)

= (8) + (7, 11)

=(7, 8, 11)

(f1.f2) ⊕ f3 = ∑ (7, 8, 11)
user
The text contains a mathematical question related to digital logic and Boolean algebra, specifically about finding the output function of a circuit with given input functions. The solution to the problem is provided in the text.

TYPE: SINGLE_QUESTION_WITH_ANSWER