11th Edition

ISBN: 9780132737968

Author: Thomas L. Floyd

Publisher: PEARSON

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Textbook Question

Chapter 4, Problem 55P

Create a table for the number of 1 s in the minterms for the expression in Problem 54 (similar to Table 4-10)

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Chapter 4, Problem 54P

Chapter 4, Problem 56P

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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. 1. (15 pts) What is the largest integer…

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1. Unsigned Integers If we have an n-digit unsigned numeral dn-1d n-2...do in radix (or base) r, then the value of that numeral is n−1 r² di Σi=0 which is basically saying that instead of a 10's or 100's place we have an r's or r²'s place. For binary, decimal, and hex r equals 2, 10, and 16, respectively. Just a reminder that in order to write down a large number, we typically use the IEC or SI prefixing system: IEC: Ki = 210, Mi = 220, Gi = 230, Ti = 240, Pi = 250, Ei = 260, Zi = 270, Yi = 280; SI: K=103, M = 106, G = 109, T = 10¹², P = 1015, E = 10¹8, Z = 1021, Y = 1024. 1.1 Conversions a. (15 pts) Write the following using IEC prefixes: 213, 223, 251, 272, 226, 244 21323 Ki8 Ki 223 23 Mi 8 Mi b. (15 pts) Write the following using SI prefixes: 107, 10¹7, 10¹¹, 1022, 1026, 1015 107 10¹ M = 10 M = 1017102 P = 100 P c. (10 pts) Write the following with powers of 10: 7 K, 100 E, 21 G 7 K = 7*10³

Chapter 4 Solutions

Digital Fundamentals (11th Edition)

Ch. 4.1 - Prob. 1CU Ch. 4.1 - Prob. 2CU Ch. 4.1 - Prob. 3CU Ch. 4.2 - Prob. 1CU Ch. 4.2 - Apply the distributive law to the expression...Ch. 4.3 - Prob. 1CU Ch. 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. 2CU Ch. 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. 2CU Ch. 4.7 - Prob. 3CU Ch. 4.8 - Prob. 1CU Ch. 4.8 - Prob. 2CU Ch. 4.8 - Prob. 3CU Ch. 4.8 - Prob. 4CU Ch. 4.9 - Lay out Karnaugh maps for three and four...Ch. 4.9 - Prob. 2CU Ch. 4.9 - Prob. 3CU Ch. 4.10 - What is the difference in mapping a POS expression...Ch. 4.10 - Prob. 2CU Ch. 4.10 - Prob. 3CU Ch. 4.11 - Prob. 1CU Ch. 4.11 - Prob. 2CU Ch. 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. 1E Ch. 4.12 - Prob. 2E Ch. 4.12 - Prob. 3E Ch. 4.12 - Prob. 4E Ch. 4.12 - Prob. 5E Ch. 4.12 - Prob. 6E Ch. 4.12 - Prob. 7E Ch. 4.12 - Prob. 8E Ch. 4.12 - Prob. 9E Ch. 4.12 - Prob. 10E Ch. 4.12 - Show the logic for segment d.Ch. 4.12 - Show the logic for segment e Ch. 4.12 - Prob. 13E Ch. 4.12 - Prob. 14E Ch. 4.12 - Prob. 15E Ch. 4 - Variable, complement, and literal are all terms...Ch. 4 - Addition in Boolean algebra is equivalent to the...Ch. 4 - Prob. 3TFQ Ch. 4 - The commutative law, associative law, and...Ch. 4 - Prob. 5TFQ Ch. 4 - When a Boolean variable is multiplied by its...Ch. 4 - Prob. 7TFQ Ch. 4 - SOP means series of products Ch. 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 language Ch. 4 - A VHDL program consists of an entity and an...Ch. 4 - Prob. 1ST Ch. 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. 5ST Ch. 4 - Prob. 6ST Ch. 4 - Prob. 7ST Ch. 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. 10ST Ch. 4 - The Boolean expression X = AB + CD represents two...Ch. 4 - An example of a sum-of-products expression is...Ch. 4 - Prob. 13ST Ch. 4 - An example of a standard SOP expression is...Ch. 4 - Prob. 15ST Ch. 4 - Prob. 16ST Ch. 4 - Prob. 17ST Ch. 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. 4P Ch. 4 - Prob. 5P Ch. 4 - Prob. 6P Ch. 4 - Prob. 7P Ch. 4 - Identify the Boolean rule(s) on which each of the...Ch. 4 - Prob. 9P Ch. 4 - Prob. 10P Ch. 4 - Prob. 11P Ch. 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. 21P Ch. 4 - Determine which of the logic circuits in Figure...Ch. 4 - Convert the following expressions to...Ch. 4 - Prob. 24P Ch. 4 - Define the domain of each SOP expression in...Ch. 4 - Prob. 26P Ch. 4 - Prob. 27P Ch. 4 - Prob. 28P Ch. 4 - Prob. 29P Ch. 4 - Prob. 30P Ch. 4 - Prob. 31P Ch. 4 - Prob. 32P Ch. 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. 37P Ch. 4 - Prob. 38P Ch. 4 - Prob. 39P Ch. 4 - Prob. 40P Ch. 4 - Prob. 41P Ch. 4 - Expand each expression to a standard SOP form:...Ch. 4 - Prob. 43P Ch. 4 - Prob. 44P Ch. 4 - Prob. 45P Ch. 4 - Use the Karnaugh map method to implement the...Ch. 4 - Solve Problem 46 for a situation in which the last...Ch. 4 - Prob. 48P Ch. 4 - Prob. 49P Ch. 4 - For the function specified in Table 4â€”16,...Ch. 4 - Determine the minimum POS expression for the...Ch. 4 - Prob. 52P Ch. 4 - Prob. 53P Ch. 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. 61P Ch. 4 - Prob. 62P Ch. 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. 68P Ch. 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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