Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter C.1, Problem 2E
Program Plan Intro
Tofind the n-input, 1-output and n-input, m-output in the given Boolean function.
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Consider a logic function with inputs A, B, and C defi ned as follows: ■ If A or C is true, then output D is true, whatever the value of B. ■ If A or B is true, then output E is true, whatever the value of C. ■ Output F is true if exactly one of the inputs is true, although we don’t care about the value of F, whenever D and E are both true. Show the full truth table for this function and the truth table using don’t cares. How many product terms are required in a PLA for each of these?
Simplify Boolean function using K map. Variables are marked in order of x,y,z.
1
d
d
0
d
1
1
1
Question 41 options:
x + y
x + y’
xz + y’
y’+z
None of the above
A Perceptron can learn the Majority function, i.e., where each input unit is a binary value (0 or 1) and it outputs 1 if there are more 1s in the input than 0s. Assume there are n input units where n is odd.
Select one:
True
False
Chapter C Solutions
Introduction to Algorithms
Ch. C.1 - Prob. 1ECh. C.1 - Prob. 2ECh. C.1 - Prob. 3ECh. C.1 - Prob. 4ECh. C.1 - Prob. 5ECh. C.1 - Prob. 6ECh. C.1 - Prob. 7ECh. C.1 - Prob. 8ECh. C.1 - Prob. 9ECh. C.1 - Prob. 10E
Ch. C.1 - Prob. 11ECh. C.1 - Prob. 12ECh. C.1 - Prob. 13ECh. C.1 - Prob. 14ECh. C.1 - Prob. 15ECh. C.2 - Prob. 1ECh. C.2 - Prob. 2ECh. C.2 - Prob. 3ECh. C.2 - Prob. 4ECh. C.2 - Prob. 5ECh. C.2 - Prob. 6ECh. C.2 - Prob. 7ECh. C.2 - Prob. 8ECh. C.2 - Prob. 9ECh. C.2 - Prob. 10ECh. C.3 - Prob. 1ECh. C.3 - Prob. 2ECh. C.3 - Prob. 3ECh. C.3 - Prob. 4ECh. C.3 - Prob. 5ECh. C.3 - Prob. 6ECh. C.3 - Prob. 7ECh. C.3 - Prob. 8ECh. C.3 - Prob. 9ECh. C.3 - Prob. 10ECh. C.4 - Prob. 1ECh. C.4 - Prob. 2ECh. C.4 - Prob. 3ECh. C.4 - Prob. 4ECh. C.4 - Prob. 5ECh. C.4 - Prob. 6ECh. C.4 - Prob. 7ECh. C.4 - Prob. 8ECh. C.4 - Prob. 9ECh. C.5 - Prob. 1ECh. C.5 - Prob. 2ECh. C.5 - Prob. 3ECh. C.5 - Prob. 4ECh. C.5 - Prob. 5ECh. C.5 - Prob. 6ECh. C.5 - Prob. 7ECh. C - Prob. 1P
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- Simplify Boolean function using K map. Variables are marked in order of xyz 1 0 1 1 1 0 1 1 Question 89 options: y’+z y’z’ + y z’+y none of teh abovearrow_forwardSimplify Boolean function using K map. Variables are marked in a,b,c,d order 0 0 1 1 0 1 1 1 1 1 1 0 1 1 0 0 Question 37 options: ac’ + ad + bd + a’c ac’ + bd’ + a’c ac’ + bd + a’c None of above c’a + b’c’ + abarrow_forwardDefine a function calc_pyramid_volume with parameters base_length, base_width, and pyramid_height, that returns as a number the volume of a pyramid with a rectangular base.Sample output with inputs: 4.5 2.1 3.0Volume for 4.5 2.1 3.0 is: 9.45Relevant geometry equations:Volume = base area x height x 1/3Base area = base length x base widthDefine a function calc_pyramid_volume with parameters base_length, base_width, and pyramid_height, that returns as a number the volume of a pyramid with a rectangular base.Sample output with inputs: 4.5 2.1 3.0Volume for 4.5 2.1 3.0 is: 9.45Relevant geometry equations:Volume = base area x height x 1/3Base area = base length x base widtharrow_forward
- Define a function calc_pyramid_volume with parameters base_length, base_width, and pyramid_height, that returns as a number the volume of a pyramid with a rectangular base.Sample output with inputs: 4.5 2.1 3.0Volume for 4.5 2.1 3.0 is: 9.45Relevant geometry equations:Volume = base area x height x 1/3Base area = base length x base widtharrow_forwardExpand to an unsimplified Boolean Function: Use CAPITAL LETTERS for the variables and APOSTROPHE (') for the OVERBAR. NO SPACES in between. Should be arrange from minterms 0 to 15. (1)sample answer: F=A'B'C'D'+ABCD'+ABCD given: F= C + ACD' + BDarrow_forwardSimplify Boolean function f=Ʃ(0,1,3) using K map. f=Ʃ(0,1,3) = _________ Question 68 options: f = x’y f = x + y’ f = x’ + y f = x’y’ + x’y + xy f = x y ‘arrow_forward
- Work out the time complexity of the function: Function f(n){ if (n>0{ x=x+1; f(n-1); f(n-1) ; f(n-1)}}arrow_forwardDefine a function calc_pyramid_volume with parameters base_length, base_width, and pyramid_height, that returns the volume of a pyramid with a rectangular base.Sample output with inputs: 4.5 2.1 3.0Volume for 4.5, 2.1, 3.0 is: 9.45Relevant geometry equations:Volume = base area x height x 1/3Base area = base length x base width.arrow_forwardWrite a simplified expression for the Boolean function defined by each of the following Kmaps: Still not sure how to get the correct answer which the book says is: x′z + x′y + xy′ + xy′z′ I keep getting X'Z + X'Y + XY'Z'arrow_forward
- Derive a truth table, product of sums representation for a function: Inputs: consist of 3 values – A, B, C – that may be either True or False Output: a single value – X – that is True when two and only two adjacent inputs are true Please produce the following; A truth table (ASCII format) for this function Derive a Sum-of-Products representation for this functionarrow_forwardExpand to an unsimplified Boolean Function: Use CAPITAL LETTERS for the variables and APOSTROPHE (') for the OVERBAR. NO SPACES in between. Should be arrange from minterms 0 to 15. Sample Answer: F=A'B'C'D'+ABCD'+ABCD F= D + AB'C + A'Darrow_forwardLet the Boolean function F(x, y, z) = x‾.(y + z) A. Find the values of the Boolean function F (you may copy the following table and fill it) B. Represent F using the sum-of-products expansion form x y z x‾ y + z x‾.(y + z) 1 1 1 1 1 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 0 0 0arrow_forward
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