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- Q1) Simplify the following Boolean functions using Karnaugh map method: A. F (D,C,B,A) =£ m(0,1,2,3,4,5,7,11,15) d (6,8,10). B. F (D,C,B,A)= E m(1,3,9,11,12,14,) d (6,7,8,10, 13).arrow_forwardQuadratic Root Solver For a general quadratic equation y = ax? + bx + c, the roots can be classified into three categories depending upon the value of the discriminant which is given by b2 - 4ac First, if the discriminant is equal to 0, there is only one real root. Then, if the discriminant is a positive value, there are two roots which are real and unequal. The roots can be computed as follows: -b+ Vb? – 4ac 2a Further, if the discriminant is a negative value, then there are two imaginary roots. In this case, the roots are given by b ь? - 4ас 2a 2a Programming tasks: A text file, coeff.txt has the following information: coeff.txt 3 4 4 4 1 4 Each line represents the values of a, b and c, for a quadratic equation. Write a program that read these coefficient values, calculate the roots of each quadratic equation, and display the results. Your program should perform the following tasks: • Check if the file is successfully opened before reading • Use loop to read the file from main…arrow_forwardF(x.y,z)=x'y'z+x'yz+xy'z'+xy'z can you simplify this and draw the diagram of the simplified functionarrow_forward
- Ql: The Collatz conjecture function is defined for a positive integer m as follows. (COO1) g(m) = 3m+1 if m is odd = m/2 if m is even =1 if m=1 The repeated application of the Collatz conjecture function, as follows: g(n), g(g(n)), g(g(g(n))), ... e.g. If m=17, the sequence is 1. g(17) = 52 2. g(52) = 26 3. g(26) = 13 4. g(13) = 40 5. g(40) = 20 6. g(20) = 10 7. g(10) = 5 8. g(5) = 16 9. g(16) = 8 10. g(8) = 4 11. g(4) = 2 12. g(2) = 1 Thus if m=17, apply the function 12 times in order to reach m=1. Use Recursive Function.arrow_forwardThe number 72 is to be represented as the sum of two positive parts, such that the product of one of the parts by the cube of the other is a maximum. It is desired to find the two parts.arrow_forward3- Simplify the following equation: f(4, B,C,D) = E(0,3,4,6,10,11,14,15) dm(2,7,8,12) where dm is denoted for don't care.arrow_forward
- Assume that an increasing function is integrable and use the properties of the integral. to prove that a decreasing function is integrable. Hint: If the function $f$ is decreasing and $g(x)=f(a)-f(x)$, then the function $g$ is increasing. CS. JG. 054arrow_forwardInterest on a credit card’s unpaid balance is calculated using the average daily balance. Suppose that netBalance is the balance shown in the bill, payment is the payment made, d1 is the number of days in the billing cycle, and d2 is the number of days payment is made before billing cycle. Then, the average daily balance is: averageDailyBalance =netBalance x d1-payment x d2d1 If the interest rate per month is, say, 0.0152, then the interest on the unpaid balance is: Interest= averageDailyBalance * 0.0152 Write a program using c++ compiler that accepts as inputnetBalance, payment, d1,d2, and interest rate per month. The program outputs the interest. Format your output to two decimal places.arrow_forwardQ11/ A function f(t) is said to be even if: Oa) f(t) = f(-t) Ob) f(t) = -f(-t) Oc) f(t) # f(-t) %3D Od) None of thesearrow_forward
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