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Chapter 3 Simplitication of tloolean Function
3-10 Simplify the following expressions in (i) stm of prociucts and (ii) products of sums
(a) \( x^{\prime} z^{\prime}+y^{\prime} z^{\prime}+y z^{\prime}+x y \) (b) \( A C^{\prime}+B^{\prime} D+A^{\prime} C D+A B C \).
(b) \( A C^{\prime}+B^{\prime} D+A^{\prime} C D+A B C D \)
3-11 Dras the AND-OR pate ime
(a) sum of products and (b) protuct of of the following function after simplifying it in
\[
F=(A, B, C, D)=2(0,2,2,6,7,8,10)
\]
3.12 Simplify the following expressions and implement them with two-level NAND gate circuits:
(a) \( A B^{\prime}+A B D+A B D^{\prime}+A^{\prime} C^{\prime} D^{\prime}+A^{\prime} B C \)
(b) \( B D+B C D^{\prime}+A B^{\prime} C^{\prime} D \)
3-13 Draw a NAND logic diagram that implements the complement of the following finction:
\[
F(A, B, C, D)=\Sigma(0,1,2,3,4,8,9,12)
\]
3.14 Draw a logic diagram using only two-input NAND gatex to implement the following expression:
\[
\left(A B+A^{\prime} B^{\prime}\right)\left(C D^{\prime}+C^{\prime} D\right)
\]
3-15 Simplify the foliowing functions and implement them with two-level NOR gate circuits (a) \( F=w x^{\prime}+y^{\prime} z^{2}+w^{\prime} y z \)
(b) \( F(w, r, y, z)=2(5,6,9,10) \)
3-16 Inplement the functions of Problem 3-15 with three-level NOR gate circuits |xiailar to Fig. 3-2I(b)].
3-17 Implement the expressions of Problem 3-12 with three-level NAND circuits |similar to Fig. 3-19(c)|
3-18 Give three possible ways to capress the function \( F \) with eight or fewer literals
\[
F(A, B, C, D)=\Sigma(0,2,5,7,10,13)
\]
3-19 Find eight different two-level gate circuits to implement
\[
F=x y^{\prime} z+x^{\prime} y z+w
\]
3-20 Implement the function \( F \) with the following twa-level forms: NAND-AND, AND NOR, OR-NAND, and NOR-OR.
\[
F(A, E, C, D)=\Sigma(0,1,2,3,4,8,9,12)
\]
3-21 List the eight degenerate two-level forms and show that they reduce to a single operation. Explain how the degenerate two-level forms can be used to extend the number of inpurs to a zute
3-22 Simplify the following Boolean functioa F together with the don't-care conditions a, then express the simplified function in sum of minterms
(a) \( F(x, y, z)=\Sigma(0,1,2,4,5) \)
\( d(x, y, z)=\Sigma(3,6,7) \)
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