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The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is
1. Y = AC+B'D'
2. Y =A'C'+B'D'
3. Y ='A''C'+'B'D
4. Y= 'A'C+'B''D'?
1. Y = AC+B'D'
2. Y =A'C'+B'D'
3. Y ='A''C'+'B'D
4. Y= 'A'C+'B''D'?
Most Upvoted Answer
The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= ...
Understanding the Problem
To simplify the given function \( Y = F(A,B,C,D) = Σm(0,2,3,6,7) + Σd(8,10,11,15) \) using a Karnaugh Map (K-map), we first plot the minterms and don't care conditions on a 4-variable K-map.
K-map Setup
1. Minterms (Σm): Place 1s in cells corresponding to minterms 0, 2, 3, 6, and 7.
2. Don't Cares (Σd): Place Xs in cells for the don't care conditions 8, 10, 11, and 15.
K-map Filling
- The K-map will look like this:
CD
00 01 11 10
+----------------
00| 1 0 0 0 | A'B'
AB 01| 1 1 1 0 | A'B
11| 0 1 1 0 | AB
10| 0 0 0 1 | AB'
Groupings and Simplification
- Group 1: 1s in cells 0, 2 (covers A'C').
- Group 2: 1s in cells 3, 7 (covers B'D).
- Don't care conditions can be used for further simplification.
Final Expression
Combining these groups yields:
- \( Y = A'C' + B'D' \)
Thus, the simplified minimal sum of products (SOP) expression for the function is:
Conclusion
- The correct answer is:
Y = A'C' + B'D'
This represents the minimal SOP derived through K-map simplification.
To simplify the given function \( Y = F(A,B,C,D) = Σm(0,2,3,6,7) + Σd(8,10,11,15) \) using a Karnaugh Map (K-map), we first plot the minterms and don't care conditions on a 4-variable K-map.
K-map Setup
1. Minterms (Σm): Place 1s in cells corresponding to minterms 0, 2, 3, 6, and 7.
2. Don't Cares (Σd): Place Xs in cells for the don't care conditions 8, 10, 11, and 15.
K-map Filling
- The K-map will look like this:
CD
00 01 11 10
+----------------
00| 1 0 0 0 | A'B'
AB 01| 1 1 1 0 | A'B
11| 0 1 1 0 | AB
10| 0 0 0 1 | AB'
Groupings and Simplification
- Group 1: 1s in cells 0, 2 (covers A'C').
- Group 2: 1s in cells 3, 7 (covers B'D).
- Don't care conditions can be used for further simplification.
Final Expression
Combining these groups yields:
- \( Y = A'C' + B'D' \)
Thus, the simplified minimal sum of products (SOP) expression for the function is:
Conclusion
- The correct answer is:
Y = A'C' + B'D'
This represents the minimal SOP derived through K-map simplification.
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The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'?
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The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'?.
The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'?.
Solutions for The simplification in minimal sum of product (SOP) of Y = F(A,B,C,D)= Σm(0,2,3,6,7) + Σ d(8,10, 11, 15) using K-maps is1. Y = AC+B'D'2. Y =A'C'+B'D'3. Y ='A''C'+'B'D4. Y= 'A'C+'B''D'? in English & in Hindi are available as part of our courses for UPSC.
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