Design a system that takes a 4-bit binary number ABCD as its input and whose output X is "1" if the decimal value of the input is equal to any of these digits (1,3,4,8), then output = 1 if the decimal value of the input is 0. A. Define your input variables and output variable and identify the relationship of the variables B. Simplify your logical expression using the minimum number of literals, if possible. Make sure to write the Boolean property/law that was done per step of simplification
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- Write a PLI program that reads in pairs of points on a Cartesian coordinate system and classifies them according to the quadrant in which they lie. Make sure you take care of the possibility that one of the pairs lies on the axes of the coordinate system.Simplify the following Boolean functions to a minimum number of literals. (a) xy+xy’ (b) (x+y)(x+y’)Asymptotic function relationships. Verify each of the following statements by the definitions to see if they are true or false 1. If f(n) = Θ(n), then nf(n) = Θ(n2 ) 2. If f(n) = O(n2 ) and g(n) = Ω(f(n)), then g(n) = O(n2) 3. If f(n) = O(0. 5n2 ) and f(n) = Ω(7n2 + nlogn), then f(n) = Θ(n2 ) 4. If f(n) = O(n3 ), then f(n) = Ω(2n3 ) 5. If f(n) = Θ(n3 ), then f(n) = O(2n )
- The function f multiplies it’s input by 8 and then subtracts 7 to produce its output. What is the symbolic representation of this operation?Given a boolean expression consisting of the symbols 0 (false), 1 (true), & (AND), I (OR), and /\ (XOR), and a desired boolean result value result, implement a function to count the number of ways of parenthesizing the expression such that it evaluates to result. The expression should be fully parenthesized (e.g., ( 0) A( 1)) but not extraneously (e.g., ( ( ( 0)) /\ ( 1)) ). EXAMPLE countEval("l/\01011", false) -> 2 countEval("0&0&0&1All0", true)-> 10When an operator is met in the postfix expression evaluation example, the two most recent operands are popped so that the subexpression may be evaluated. The first popped operand is handled as the second operand in the subexpression, whereas the second popped operand is the first. Give and explain an example of how this component of the solution is important.
- Simplify or reduce the Boolean function below into three literals: F(P,Q,R) = (P + Q’R’)(PQ+R)+PQR’+P’R3. Give the regular expression, NFA, and DFA for L, = {w: w ends in 00 or 01}, where Σ (0, 1 .Program to be written in C A palindrome is a word or a phrase that is the same when read both forward and backward. Examples are: "bob," "sees," or "never odd or even" (ignoring spaces). Write a program whose input is a word or phrase, and that outputs whether the input is a palindrome. You may assume that the input string will not exceed 50 characters. Ex: If the input is bob, the output is: bob is a palindrome Ex: If the input is bobby, the output is: bobby is not a palindrome Hint: Start by just handling single-word input, and submit for grading. Once passing single-word test cases, extend the program to handle phrases. If the input is a phrase, remove or ignore spaces.
- Consider the infix expression exp = ( ( 8 / 2 ) + 3 ) * 1 to solve the questions given below: a: Trace the process of converting the infix expression into It's postfix form. b: Evaluate the postfix expression you obtained in part a. *************************************************************************************** Note: Solve the question in your notebook. Draw two tables as shown below. Scan or take a picture, upload the file. a: Next token Action Content of stack Postfix expression b: Next token Action Content of stackGive an example of a while loop, then provide the equivalent do-while loop and for loop. Then give a different example of a do-while loop, along with the equivalent while loop and for loop. Finally, give an example of a for loop, along with the equivalent while loop and do-while loop. Use your examples to illustrate the advantages and disadvantages of each looping structure, and describe those advantages and disadvantages.Help Me With C Programming On their way down the river, Jojo and Lili saw two frogs in X1 and X2 respectively. The two frogs are seen jumping up and down happily in the same direction, which is coming to Jojo. After noticing the two frogs, Jojo and Lili noticed that the speed of the two frogs was different. The first frog to start jumping from the X1 position has a speed of V1, while the second frog that starts jumping from the X2 position has a V2 speed. Jojo guessed that the "YES" of the two frogs would be in the same position in a given T time, while Bibi guessed the "NO" of the two frogs would never be in the same position in that time. Help Jojo and Lili take into account the frog's movements to determine if their guess is correct. Format Input The first line of input consists of a series of integers namely X1, V1, X2, V2, T. X1 and V1 are the starting positions and jumping speeds per second of the first frog. X2 and V2 are the starting positions and jumping speeds per second…