9. Prove the following Boolean algebra. (A+B)(A+C) = A + BC ABC + ABC + ABC = A(B+C) (i) (ii)
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- Convert the following boolean equation to a circuit schematic (and select the correct circuit below): F(a,b,c)=a'b'c'+a'bc+ab'c'+abc'Subject: Differential Equation Please see the image attached. There are typographical errors, the units are not micro farad, they are micro coulombs.Simplify the following expressions using Karnaugh map. Provide a complete and legible solution. 1. F(A,B,C,D) = A’B’C’ + B’CD’ + A’BCD’ + AB’C’
- An 8 × 1 multiplexer has inputs A, B, and C connected to the selection inputs S 2 , S 1 , and S 0 , respectively. The data inputs I 0 through I 7 are as follows:1. (a) I 1 = I 2 = I 7 = 0 ; I 3 = I 5 = 1 ; I 0 = I 4 = D ; and I 6 = D ′ .2. (b) I 1 = I 2 = 0 ; I 3 = I 7 = 1 ; I 4 = I 5 = D ; and I 0 = I 6 = D′ . Determine the Boolean function that the multiplexer implements.Using K - Map , simplify the following Boolean expression : X = ( 5,8,9,11,14 )8. Simplify the given function using K-Map. Y (A, B, C, D) =∑m (0,2,4,7,8,10,12) +d (5,6,13,14).
- F3=A’B’C’+A’BC’+ABC’+AB’C’+A’BC Simplify their function using Boolean algebra axioms and theorems.Calculate y(t)=x(t)*v(t) using the convolution integral for the continuous signals x(t) and v(t) given in the figure below. Write the result of y(t) as a piecewise function. Also, show the result in an approximate way by drawing a graph.Find the state and output equations for the electrical network shown if the output vector is y = [V_r2 , i_r2]^T