Digital Fundamentals (11th Edition)
11th Edition
ISBN: 9780132737968
Author: Thomas L. Floyd
Publisher: PEARSON
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Chapter 4, Problem 48P
a)
Program Plan Intro
To minimize the expression
Program Plan Intro
To minimize the expression
Program Plan Intro
To minimize the expression
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Write the following Boolean function in disjunctive normal formF(x, y, x) = (x + ¯y)(¯x + ¯z).
Build the Karnaugh map for each of the following expressions:
A(BC + BC) + A(BC + BC)
●
ABCD + ABCD + ABCD + ABCD
Q. Use K-maps to convert the following standard POS expression into:
a) a minimum POS expression, b) a standard SOP expression, and
c) a minimum SOP expression.
F = (A+B+C+D)(A+B+C+D)(A+B+C+D)(A+B+C+D)(A+B+C+D)(A+B+C +D)
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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- g Boolean Function: F(w,x,y,z) = (8,10,12,14)arrow_forwardGiven the following truth table, write an algebraic expression for the given function andsimplify the expression using a Karnaugh map.A B C F0 0 0 10 0 1 10 1 0 10 1 1 01 0 0 01 0 1 11 1 0 01 1 1 1arrow_forwardFor the given truth table for Function F in three variables:arrow_forward
- Q1 (a) Convert the following expression into Product of Sum (POS) expression. Simply the obtain POS expression using Karnaugh-map. X = ABC + ABC+ABC+A B C + ABCarrow_forward47. Use a Karnaugh map to simplify each expression to minimum POS form: (a) (A + B + C + D)(A + B + C + D)(A + B + C + D) (b) (X + Y)(W + Z)(X + Y + Z)(W + X + Y + Z) 48. For the function specified in the truth table of Figure 4-59, determine the minimum POS expression using a Karnaugh map. 49. Determine the minimum POS expression for the function in the truth table of Figure 4-60. 50. Convert each of the following POS expressions to minimum SOP expressions using a Karnaugh map: (a) (A + B)(A + C)(A + B + C) (b) (A + B)(A + B + C)(B + C + D)(A + B + C + D)arrow_forward7. Write the simplified (minimized) expression for the Boolean function defined by the following Karnaugh Map (KMap) in Sum of Product (SOP) form. WX yz 00 01 11 10 00 0 0 1 1 01 1 1 1 1 11 0 1 0 0 10 1 1 0 1arrow_forward
- Represent the standard form of the expression with Karnaugh Maparrow_forward12 The simplified Boolean function in SoP, which is obtained from F (A,B, C) = 7 (2, 3, 4, 5, 6, 7) is: AB + A'B' None A'B'C' АВ A'B'arrow_forwardSimplify following Boolean Expressions using Quine-McClukey tabular method. F(A_B_CDEF=Sm(6,9,13,18,19,25,27,29,41,45,57,61)arrow_forward
- Use a Karnaugh map to minimize the following standard POS expression: F = (A+B+C)(A+ B+ C)(A+B+C)(A+B+C)(A + B+C)arrow_forwardFind the minterms of the following Boolean expressions by first plotting each function in a K-map: wyz+w′x′+wxz′arrow_forwardUse a Karnaugh map to find the minimal sum for the following expression: F = ābcd + ābēd + abcd + ābēd + ābcd + ābcdarrow_forward
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