Please show working on paper. Logisim isn’t required

 

2)Assume that you want to invest a large amount of money into the stock market and do not trust just anyone to give you advice about buying and selling stocks. Fortunately, you have four reliable sources from which you can gain valuable advice. The first source is your Mom (M), the second source is Warren Buffet (W), a self-made billionaire in the stock market, the third is Donald Trump (D), and the fourth source is Fido (F), world famous psychic dog. After several months of receiving advice from all four, you have come to the following conclusions:

 

       a. Buy if your Warren Buffet and Fido both say yes

       b. Buy if at least three of the four say yes

       c. Buy if Warren Buffet and your Mom, or Donald Trump says yes.

       d. Don’t buy if your Mom and one other person says no (this has precedence over any previous Buy recommendation)

        Using the circuit design procedure discussed in the notes, design with a truth-table (using inputs M, W, D, F), simplify with K-maps, and draw the logic circuit that tells when to buy a stock.

 

 3) Using the combinational circuit design procedure discussed in the notes, design with a truth-table, simplify with K-maps, and draw the combinational circuit that accepts a 3-bit number and generates a 5-bit number output equal to 4X + 1 where X is the input number. Let the inputs be A, B, C and the outputs be V, W, X, Y, Z.

 

4) From the following functions, create the truth table, simplify with a K-Map, and then implement with two-level NAND gate circuits (only use NAND gates).

a) F1 (A,B,C,D) = A’B + ABC + B’C’D + AB’D + C’D

b) F2 (A,B,C,D) = (A’ + B + C’) (A’ + B)(A + D’)

 

5) A combinational circuit is specified by the following three Boolean functions:

                                   F1 (a,b,c) = G(2,4,7)

                                   F2 (a,b,c) = G(0,1,4,6)

                                     F3 (a,b) = G(1,3)

Implement the circuit with a decoder (use block diagram for the decoder ... that is, you do not need to show the internal circuitry of the decoder)

 

 6) Design and build a circuit with 3 inputs (a, b, c) and 3 outputs (X, Y, Z) where the outputs are negation of the input binary number (i.e. flip the 0's to 1's and 1's to 0's and then add one ... if the input is 101, then the output would be 011)

 (a) Implement this with AND/OR/NOT gates. Show the Truth Table, K-maps, and circuit.

 (b) Implement this with a decoder. Show the circuit.

 

7) Using a multiplexor, implement the function F(a,b,c,d) = G(0,1,3,6,8,10,11,13) assuming we connect:

 a) a, b and c to the selector lines (S2 , S1 , S0 respectively)

 b) b, a and d to the selector lines (S2 , S1 , S0 respectively)