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GO Classes 2023 | IIITH Mock Test 1 | Question: 39

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Consider a $4$ input boolean function $\mathrm{F}(\mathrm{X}, \mathrm{Y}, \mathrm{Z}, \mathrm{T})$.

The minterm $\mathrm{X}^{\prime} \mathrm{Y}^{\prime} \mathrm{Z}^{\prime} \mathrm{T}^{\prime}$ is known to be in the SOP form of $\mathrm{F}$. Canonical SOP form of function $F$ itself is the minimized SOP form of $F,$ and $F$ is largest such function i.e. Canonical SOP form of $F$ has maximum number of minterms possible. Which of the following is/are True?

  1. Number of Prime Implicants in $F$ is the same as the number of prime implicants in $F'.$
  2. Minimized SOP, Minimized POS form of $F$ have the same number of literals.
  3. Every implicant of $F$ is a Prime Implicant.
  4. $\mathrm{F}=\mathrm{X} \oplus \mathrm{Y} \oplus \mathrm{Z} \oplus \mathrm{T}$
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The maximum number of minterms that the SOP form of $F$ can have such that no simplification is possible (i.e. Canonical SOP form itself is the minimized SOP form) is $8.$
The following set of True Minterms for function F will lead to No simplification of Canonical SOP possible.
$0,3,5,6,9,10,12,15$
Note that F' also cannot be simplified.
$\mathrm{F}^{\prime}=\mathrm{X} \oplus \mathrm{Y} \oplus \mathrm{Z} \oplus \mathrm{T}$
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GO Classes 2023 | IIITH Mock Test 1 | Question: 34
The possible number of Boolean function of 3 variables $X, Y$ and $Z$ such that $f(X, Y, Z)=f\left(X^{\prime}, Y^{\prime}, Z^{\prime}\right)$ $8$ $16$ $64$ $32$
The possible number of Boolean function of 3 variables $X, Y$ and $Z$ such that $f(X, Y, Z)=f\left(X^{\prime}, Y^{\prime}, Z^{\prime}\right)$$8$$16$$64$$32$
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