1) Consider bit strings of 3 bits b2 b1 b0. Develop a proposition R expressed in...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1) Consider bit strings of 3 bits b2 b1 b0. Develop a proposition R expressed in terms of b0, b1, and b2 which is true (T) for such a bit string if and only if b2 b1 b0 = b0 b1 b2, i.e., if the bit string b2 b1 b0 is equal to its reverse. For example, R should be true (T) for bit string 010, but false F for bit string 001. Simplify you proposition as much as possible using the replacements laws of propositional logic. 2) Suppose that you have 2 two-bit bit strings a and b. Think of a as a1a0 and b as b1b0. So a(and, similarly b) represent the natural numbers 0, 1, 2, and 3 as the bit strings 00,01, 10, and 11, respectively. Design a proposition L in terms of a0, a1, b0, and b1 such that L is true if and only if a b. For example, L should be true (T) when a = 10 and b = 11, L should be false when a= 01 and b = 00, and L should also be true when a = 01 and b = 01. Simplify you proposition as much as possible using the replacements laws of propositional logic. 3) Suppose that you have 2 two-bit bit strings a and b. Think of a as a1a0 and b as b1b0. So a and b represent the numbers 0, 1, 2, and 3 as the bit strings 00, 01, 10, and 11, respectively. Design 2 propositions in terms of a0, a1, b0, and b1 that "implement" the function max (0, a-b). So for example max(0,3-0) = 3 and max(0,1-2) = 0. Notice that you need 2 propositions since max ranges from 0 to 3. Simplify your propositions as much as possible using the replacement laws. 1) Consider bit strings of 3 bits b2 b1 b0. Develop a proposition R expressed in terms of b0, b1, and b2 which is true (T) for such a bit string if and only if b2 b1 b0 = b0 b1 b2, i.e., if the bit string b2 b1 b0 is equal to its reverse. For example, R should be true (T) for bit string 010, but false F for bit string 001. Simplify you proposition as much as possible using the replacements laws of propositional logic. 2) Suppose that you have 2 two-bit bit strings a and b. Think of a as a1a0 and b as b1b0. So a(and, similarly b) represent the natural numbers 0, 1, 2, and 3 as the bit strings 00,01, 10, and 11, respectively. Design a proposition L in terms of a0, a1, b0, and b1 such that L is true if and only if a b. For example, L should be true (T) when a = 10 and b = 11, L should be false when a= 01 and b = 00, and L should also be true when a = 01 and b = 01. Simplify you proposition as much as possible using the replacements laws of propositional logic. 3) Suppose that you have 2 two-bit bit strings a and b. Think of a as a1a0 and b as b1b0. So a and b represent the numbers 0, 1, 2, and 3 as the bit strings 00, 01, 10, and 11, respectively. Design 2 propositions in terms of a0, a1, b0, and b1 that "implement" the function max (0, a-b). So for example max(0,3-0) = 3 and max(0,1-2) = 0. Notice that you need 2 propositions since max ranges from 0 to 3. Simplify your propositions as much as possible using the replacement laws.
Expert Answer:
Related Book For
Business Statistics In Practice
ISBN: 9780073401836
6th Edition
Authors: Bruce Bowerman, Richard O'Connell
Posted Date:
Students also viewed these programming questions
-
In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Economist Abba Lerner proposed a tariff on oil imports equal to 100 percent of the import price. This tariff is designed to reduce dependence on foreign sources as well as to discourage OPEC from...
-
Modify the pervious query to that instead of displaying as one of the totals the total number pounds of milk produced in each region, the total number of pounds of milk produced in each year across...
-
Show that Lagranges interpolation formula for cubic interpolation is Use this formula to find a cubic polynomial that fits the function f given in the following table: Draw the graph of the cubic for...
-
The magnitude of the gravitational force exerted by Earth on an object of inertia \(m_{1}\) is \(m_{1} g\). (a) What is the magnitude of the force exerted by the object on Earth (inertia...
-
Bolds Gym, a health club chain, is considering expanding into a new location: the initial investment would be $1 million in equipment, renovation, and a 6-year lease, and its annual upkeep and...
-
1. Which of the following is a CORRECT statement? 2. 3. (a) 2.3056+10.138-7.4671 = 4.9765 (b) 2.38 x 1.0 = 2.38 8.05 (c) -=2.6 3.1 (d) (1.11 0.1) x 9.0 = 9.0 A projectile travels at 0 below...
-
An organisation with basic values and beliefs that encourage people within the company to behave well has A. Corporate responsibility B. A corporate code of ethics C. An ethical culture
-
There are two 3-L bottles, one filled with water and the other filled with milk. Which one will have higher inertia?
-
Two identical boxes A and B slide over the same rough floor. Box B stops over a distance twice as long as that needed for box A. Assuming a constant frictional force \(F\) acting in both cases,...
-
The engine of a moving spaceship suddenly stopped working. What will happen to the motion of the space ship?
-
Besides layoffs, what other options might the executives have tried to reduce costs?
-
The boiling point of water on top of a mountain reduced to \(80^{\circ} \mathrm{C}\) compared to \(100^{\circ} \mathrm{C}\) at the sea level. Is the boiling point of water intensive or extensive?
-
The methodology section is a major section of your research paper and, as such, is preceded by a level one heading formatted in accordance with the requirements in the Publication Manual entitled...
-
1. Firms may hold financial assets to earn returns. How the firm would classify financial assets? What treatment will such financial assets get in the financial statements in accordance with US GAAP...
-
How far above Farth's surface must a \(10,000-\mathrm{kg}\) boulder be moved to increase the mass of the Earthboulder system by \(2.50 \mathrm{mg}\) ? Assume the same ratio of energy change to mass...
-
Is an oscillating object in translational equilibrium?
-
Show that for small displacements the restoring force exerted on part 2 of the displaced string in Figure 15.14 is linearly proportional to the displacement of that part from its equilibrium...
Study smarter with the SolutionInn App