Файл: Digital design with CPLD applications and VHDL (R. Dueck, 2000).pdf
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3.15Write the POS form of the 2-input XOR function. Draw the logic diagram of the POS form of the XOR function.
3.16Write the POS form of the 2-input XNOR function. Draw the logic diagram of the POS form of the XNOR func-
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tion.
Section 3.3 Theorems of Boolean Algebra
3.17Write the Boolean expression for the circuit shown in Figure 3.65 Use the distributive property to transform the circuit into a sum-of-products (SOP) circuit.
3.18Write the Boolean expression for the circuit shown in Figure 3.66 Use the distributive property to transform the circuit into a sum-of-products (SOP) circuit.
3.19Use the rules of Boolean algebra to simplify the follow-
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FIGURE 3.65
Problem 3.17
Logic Circuit
ing expressions as much as possible.
a. Y A A B C
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FIGURE 3.66
Problem 3.18
Logic Circuit
Problems 109
b.Y A A B C
c.J K L L
d.S (T U) V V
e.S T V V
f.Y (A B C)(B D F)
3.20Use the rules of Boolean algebra to simplify the following expressions as much as possible.
a.M P Q P Q R
b.M P Q P Q R
c.S (T U ) V (T U)
d.Y (A B D) A C A B D
e.Y (A B D) A C A B D
f.P (Q R S T )(Q R Q)
g.U (X Y W Z)(W Y Y W Z)
3.21Use the rules of Boolean algebra to simplify the following expressions as much as possible.
a.Y A B C D (A B) C D A B
b.Y A B C D (A B) C D A B
c.K (L M L M )(M N L M N) M(N L)
Section 3.4 Simplifying SOP and POS Expressions
3.22Use the rules of Boolean algebra to find the maximum SOP and POS simplifications of the function represented by the following truth table.
3.23Use the rules of Boolean algebra to find the maximum SOP and POS simplifications of the function represented by the following truth table.
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3.24Use the rules of Boolean algebra to find the maximum SOP and POS simplifications of the function represented by the following truth table.
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110 C H A P T E R 3 • Boolean Algebra and Combinational Logic
3.25Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth table.
3.28Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth table.
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3.26Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth table.
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3.27Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth table.
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3.29Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth table.
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3.30Use the rules of Boolean algebra to find the maximum SOP simplification of the function represented by the following truth table.
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Section 3.4 Simplification by the Karnaugh Map Method
3.31Use the Karnaugh map method to find the maximum SOP
A B C D Y
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simplification of the logic diagram in Figure 3.21.
3.32Use the Karnaugh map method to reduce the following Boolean expressions to their maximum SOP simplifications:
a.Y A B C A B C A B C
b.Y A B C A B C A B C A B C A B C
c.Y A B C A B C A B C A B C
d.Y A B C D A B C D A B C D A B C D
A B C D A B C D A B C D A B C D
A B C D
3.33Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
3.34Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
Problems 111
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3.35Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
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3.36Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
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112 C H A P T E R 3 • Boolean Algebra and Combinational Logic
3.37Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
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3.38Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
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3.39Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
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3.40Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.
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3.41Use the Karnaugh map method to reduce the Boolean expression represented by the following truth table to simplest SOP form.