Given the following truth table, write an algebraic expression for the given function and simplify the expression using a Karnaugh map. A В C F 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Find the minimum sum-of-products expression for each function. (a) f(a, b, c, d) = E m(0, 2, 3, 4, 7, 8, 14) (b) f(a, b, c, d) = E m(1.2,4, 15) +E d(0, 3, 14) (c) f(a, b, c, d) = II M(1, 2,3, 4, 9, 15) (d) f(a, b, с, d) %3D П М(0, 2, 4, 6, 8) П D(1, 12, 9, 15) 5.7 П М(1,2, 3,4, 9, 15)

3.) Given this truth table, find the unoptimized formula this corresponds to, along with the version which was optimized with a K-Map. A B C D O 0 0 0 0 0 0 0 1 0 0 1 0 0 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 1 1 1 1 0 0 0 1 0 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 0 0 0 Unoptimized Sum of Products equation 3a) 0 = Draw the K-map and simplify Optimized Sum of Products equation 3b) 0 =

3. (1 pt) Simplify the Boolean function using K-map. AB 00 01 11 10 1 1 1 1

1, 2

1) The truth table of function fis given below left. Please complete its k-map in the right. XI X2 X3 X3

Using the three-variable Karnaugh-map below Solve for its corresponding function expression Replot the function from part (1) on a different three-variable Karnaugh-map (Hint: try a different combination of variables)

Q1 Find the minimum sum-of-products expression for each function (d denotes don't care terms specified in parentheses). (a) f(a,b,c,d) = Σm(0,2,3,4,7,8,14) (b) f(a,b,c,d) = Σm(1,2,4,15) + Σd(0,3,14)

2. Assume you have the following truth tables for functions F1(x, y, z) and F2(x, y, z): X y 0 0 0 0 1 1 1 1 oK NOH 0 0 0 1 1 1 0 0 0 1 1 0 1 1 0 F1 --| 1 1 0 0 0 1 0 0 F2 ононононл 1 1 1 1 a) Express F1 and F2 in sum-of-products form b) Simplify each function

Compute the following values of ψ(X, B), the number of B-smooth numbers between 2 and X. (c) ψ(50, 7)

1. Given the following truth table: с F 1 A В 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 a) Write down the minterm expansion for the function F b) Draw the K-Map using the minterm expansion

f(x) = -1.26 – 1.5x + x2 Find the root of the function by using one of the open methods or bracket methods with relative errors ea smaller than the maximum relative error ea = 0.001% (using matlab)

Draw the graph of the function f(x)=⌊x/2⌋ from R to R.