Digital Fundamentals (11th Edition)
11th Edition
ISBN: 9780132737968
Author: Thomas L. Floyd
Publisher: PEARSON
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Textbook Question
Chapter 4.12, Problem 1CU
What are the advantages of Boolean logic simplification in terms of writing a VHDL
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2. Signed Integers
Unsigned binary numbers work for natural numbers, but many calculations use negative
numbers as well. To deal with this, a number of different methods have been used to represent
signed numbers, but we will focus on two's complement, as it is the standard solution for
representing signed integers.
2.1 Two's complement
• Most significant bit has a negative value, all others are positive. So, the value of an n-digit
-2
two's complement number can be written as: Σ2 2¹ di 2n-1 dn
• Otherwise exactly the same as unsigned integers.
i=0
-
• A neat trick for flipping the sign of a two's complement number: flip all the bits (0 becomes 1,
or 1 becomes 0) and then add 1 to the least significant bit.
• Addition is exactly the same as with an unsigned number.
2.2 Exercises
For questions 1-3, answer each one for the case of a two's complement number and an
unsigned number, indicating if it cannot be answered with a specific representation.
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Chapter 4 Solutions
Digital Fundamentals (11th Edition)
Ch. 4.1 - Prob. 1CUCh. 4.1 - Prob. 2CUCh. 4.1 - Prob. 3CUCh. 4.2 - Prob. 1CUCh. 4.2 - Apply the distributive law to the expression...Ch. 4.3 - Prob. 1CUCh. 4.4 - Replace the AND gates with OR gates and the OR...Ch. 4.4 - Construct a truth table for the circuit in...Ch. 4.5 - Simplify the following Boolean expressions:...Ch. 4.5 - Implement each expression in Question 1 as...
Ch. 4.6 - Identify each of the following expressions as SOP,...Ch. 4.6 - Prob. 2CUCh. 4.6 - Convert each POS expression in Question 1 to...Ch. 4.7 - If a certain Boolean expression has a domain of...Ch. 4.7 - Prob. 2CUCh. 4.7 - Prob. 3CUCh. 4.8 - Prob. 1CUCh. 4.8 - Prob. 2CUCh. 4.8 - Prob. 3CUCh. 4.8 - Prob. 4CUCh. 4.9 - Lay out Karnaugh maps for three and four...Ch. 4.9 - Prob. 2CUCh. 4.9 - Prob. 3CUCh. 4.10 - What is the difference in mapping a POS expression...Ch. 4.10 - Prob. 2CUCh. 4.10 - Prob. 3CUCh. 4.11 - Prob. 1CUCh. 4.11 - Prob. 2CUCh. 4.12 - What are the advantages of Boolean logic...Ch. 4.12 - How does Boolean logic simplification benefit a...Ch. 4.12 - Name the three levels of abstraction for a...Ch. 4.12 - Prob. 1ECh. 4.12 - Prob. 2ECh. 4.12 - Prob. 3ECh. 4.12 - Prob. 4ECh. 4.12 - Prob. 5ECh. 4.12 - Prob. 6ECh. 4.12 - Prob. 7ECh. 4.12 - Prob. 8ECh. 4.12 - Prob. 9ECh. 4.12 - Prob. 10ECh. 4.12 - Show the logic for segment d.Ch. 4.12 - Show the logic for segment eCh. 4.12 - Prob. 13ECh. 4.12 - Prob. 14ECh. 4.12 - Prob. 15ECh. 4 - Variable, complement, and literal are all terms...Ch. 4 - Addition in Boolean algebra is equivalent to the...Ch. 4 - Prob. 3TFQCh. 4 - The commutative law, associative law, and...Ch. 4 - Prob. 5TFQCh. 4 - When a Boolean variable is multiplied by its...Ch. 4 - Prob. 7TFQCh. 4 - SOP means series of productsCh. 4 - Karnaugh maps can be used to simplify Boolean...Ch. 4 - A4-variable Karnaugh map has eight cells.Ch. 4 - VHDL is a type of hardware definition languageCh. 4 - A VHDL program consists of an entity and an...Ch. 4 - Prob. 1STCh. 4 - The Boolean expression A + B + C is a sum term a...Ch. 4 - The Boolean expression ABCD is a sunn term a...Ch. 4 - The domain of the expression ABCD+AB+CD+B A and D...Ch. 4 - Prob. 5STCh. 4 - Prob. 6STCh. 4 - Prob. 7STCh. 4 - Which one of the following is not a valid rule of...Ch. 4 - Which of the following rules states that if one...Ch. 4 - Prob. 10STCh. 4 - The Boolean expression X = AB + CD represents two...Ch. 4 - An example of a sum-of-products expression is...Ch. 4 - Prob. 13STCh. 4 - An example of a standard SOP expression is...Ch. 4 - Prob. 15STCh. 4 - Prob. 16STCh. 4 - Prob. 17STCh. 4 - VHDL is a type of programmable logic hardware...Ch. 4 - In VHDL, a port is a type of entity a type of...Ch. 4 - Using VDHL, a logic circuits inputs and outputs...Ch. 4 - Using Boolean notation, write an expression that...Ch. 4 - Write an expression that is a 1 only if all of its...Ch. 4 - Write an expression that is a 1 when one or more...Ch. 4 - Prob. 4PCh. 4 - Prob. 5PCh. 4 - Prob. 6PCh. 4 - Prob. 7PCh. 4 - Identify the Boolean rule(s) on which each of the...Ch. 4 - Prob. 9PCh. 4 - Prob. 10PCh. 4 - Prob. 11PCh. 4 - Write the Boolean expression for each of the logic...Ch. 4 - Write the Boolean expression for each of the logic...Ch. 4 - Draw the logic circuit represented by each of the...Ch. 4 - Draw the logic circuit represented by each...Ch. 4 - Draw a logic circuit for the case where the...Ch. 4 - Develop the truth table for each of the circuits...Ch. 4 - Construct a truth table for each of the following...Ch. 4 - Using Boolean algebra techniques, simplify the...Ch. 4 - Using Boolean algebra, simplify the following...Ch. 4 - Prob. 21PCh. 4 - Determine which of the logic circuits in Figure...Ch. 4 - Convert the following expressions to...Ch. 4 - Prob. 24PCh. 4 - Define the domain of each SOP expression in...Ch. 4 - Prob. 26PCh. 4 - Prob. 27PCh. 4 - Prob. 28PCh. 4 - Prob. 29PCh. 4 - Prob. 30PCh. 4 - Prob. 31PCh. 4 - Prob. 32PCh. 4 - Develop a truth table for each of the SOP...Ch. 4 - Develop a truth table for each of the standard POS...Ch. 4 - Develop a truth table for each of the standard POS...Ch. 4 - For each truth table in Table 4-15 0, derive a...Ch. 4 - Prob. 37PCh. 4 - Prob. 38PCh. 4 - Prob. 39PCh. 4 - Prob. 40PCh. 4 - Prob. 41PCh. 4 - Expand each expression to a standard SOP form:...Ch. 4 - Prob. 43PCh. 4 - Prob. 44PCh. 4 - Prob. 45PCh. 4 - Use the Karnaugh map method to implement the...Ch. 4 - Solve Problem 46 for a situation in which the last...Ch. 4 - Prob. 48PCh. 4 - Prob. 49PCh. 4 - For the function specified in Table 4—16,...Ch. 4 - Determine the minimum POS expression for the...Ch. 4 - Prob. 52PCh. 4 - Prob. 53PCh. 4 - List the minterms in the expression...Ch. 4 - Create a table for the number of 1 s in the...Ch. 4 - Create a table of first level minterms for the...Ch. 4 - Create a table of second level minterms for the...Ch. 4 - Create a table of prime implicants for the...Ch. 4 - Determine the final reduced expression for the...Ch. 4 - Write a VHDL program for the logic circuit in...Ch. 4 - Prob. 61PCh. 4 - Prob. 62PCh. 4 - Explain the purpose of the invalid code detector.Ch. 4 - For segment c, how many fewer gates and inverters...Ch. 4 - Repeat Problem 64 for the logic for segments d...Ch. 4 - The logic for segments b and c in Figure 4-53...Ch. 4 - Redesign the logic for segment a in the Applied...Ch. 4 - Prob. 68PCh. 4 - Design the invalid code detector.Ch. 4 - Open file P04-70. For the specified fault, predict...Ch. 4 - Open file P04-71. For the specified fault, predict...Ch. 4 - Open file P04-72. For the observed behavior...
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