Digital circuits miscellaneous
- The logic circuit given below converts a binary code Y1 Y2 Y3 into
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In Gray code successive Code words differ by the complementation of a single bit and this logic has been complemented in the given circuit.
Correct Option: B
In Gray code successive Code words differ by the complementation of a single bit and this logic has been complemented in the given circuit.
- Venn diagram representing the Boolean expression A + (A. B) is
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NA
Correct Option: A
NA
- The logic function ƒ = (x . y) + (x.y) is the same as
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ƒ = x ⊕ y = x ⊙ y = xy + xy
Correct Option: B
ƒ = x ⊕ y = x ⊙ y = xy + xy
- The minimal product-of-sums function described by the K-map given in the figure is, φ don’t care
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NA
Correct Option: A
NA
- I n the given network of AND and OR gates, ƒ can be written as
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In terms of Boolean operations
Output of 1 is x0 x1
Output of 2 is (x0 x1 + x2)
Output of 3 is (x0 x1 + x2) x3 = x0 x1 x3 + x2 x3
Output of 4 is x0 x1 x3 + x2 x3 + x4
Output of 5 would be x0 x1 x3 x5 + x2 x3 x5 + x4 x5
Output of 6 would be x0 x1 x3 x5 + x2 x3 x5 + x4 x5 x6
Thus for n gates connected as shown, the output would be
x0 x1 x3 ...................... xn– 1
+ x2 x3 x5 ...................... xn– 1
+ x4 x5 x7 ...................... xn– 1
+ xh – 2 xn– 1
+ xn .Correct Option: D
In terms of Boolean operations
Output of 1 is x0 x1
Output of 2 is (x0 x1 + x2)
Output of 3 is (x0 x1 + x2) x3 = x0 x1 x3 + x2 x3
Output of 4 is x0 x1 x3 + x2 x3 + x4
Output of 5 would be x0 x1 x3 x5 + x2 x3 x5 + x4 x5
Output of 6 would be x0 x1 x3 x5 + x2 x3 x5 + x4 x5 x6
Thus for n gates connected as shown, the output would be
x0 x1 x3 ...................... xn– 1
+ x2 x3 x5 ...................... xn– 1
+ x4 x5 x7 ...................... xn– 1
+ xh – 2 xn– 1
+ xn .
