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 30.3, Problem 2E
Program Plan Intro
To show that how to find implement a FFT
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Implement the given notation using multiplexer:
H (K,J,P,O) = ∑ (0,1,3,5,6,10,13,14)
Include the truth table and multiplexer implementation.
A circuit has four inputs p,q,r,s representing the natural binary number 0000=0,to 1111=15 p is the most significant bit .the circuit has one output, x,which is true if the input to the circuit represent is a prime number and false other wise (A) design a true table for this circuit, and hence obtain an expression for x in terms of P,Q,R,S.
Which statement below best describes a Karnaugh map?
O a. A Karnaugh map can be used to replace Boolean rules
O b. Variable complements can be eliminated by using Karnaugh maps
Oc tis simply a rearranged truth table
O d. The Karnaugh map eliminates the need for using NAND and NOR gates
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- Using a multiplexer, implement the Boolean Function F(A,B,C,D) = Sum_m(3,7,11,12,13,14,15) with select lines A,C, and D? What is the optimum size of the MUX?arrow_forwardDesign a Mealy-type FSM that detects a sequence of four or more consecutive 1's in a string of bits coming through an input line. Draw out the state diagram, the state table, and state-assigned table; then, synthesize the circuit. An example of the desired behavior is: w: 0011110111110 z: 0000010000110arrow_forwardConvert the expression below to canonical form (Product of Maxterms). Express your answer in short notation (IIm). F (W, X,Y, Z) = (X' +Y +Z)(X' +Z)(X+Y)arrow_forward
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- . Given the function: F(a, b, c) = (a + b)’c + a b c’ + a c a) Create the truth table for function F. 7b) Implement F by means of an 8-to-1 Multiplexer using block diagrams. Implement F by means of a 3-to-8 Decoder using block diagrams and any gates if needed.arrow_forwardIn designing of a binary counter with states A (MSB) and B (LSB), the derived input equations are as follows TA = BOx and TB =1. Where x is input. When x = 0, the counter counts Oa. AB: none of these O b. AB: 11--> 01 -->10 --> 00 --> 11 O c. AB: 11-->10 --> 01 --> 00 -->11 O d. AB: 00 --> 01 --> 10 --> 11--> 00arrow_forwardGiven the following Boolean expression F (A, B, C, D) = AB'C (BD + C’D) + AC' Convert the given expression F into standard SoP form (Minterms). Find the equivalent expression of F in standard PoS form (Maxterms). Find the complement of F i.e. and write the expression for in standard PoS form (Maxterms).arrow_forward
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