Complete the following mintermmaxterm equations and then

Question

Assignment: Logic Circuits and Assignment Statement Name:

Designing with VHDL

1. Write two VHDL assignment statements to implement the circuits displayed below:

F <=
G <=

2. In a logic function with n inputs, there are 2ⁿ unique combinations of inputs and 2^{2^n} possible logic functions. The table below has four rows that show the four possible combinations of two inputs (2² = 4), and 16 output columns that show all possible two-input logic functions (2^{2^n}=16). Six of these output columns are associated with common logic functions of two variables.

Circle the six columns, label them with the appropriate logic gate name, and draw the logic gate symbols for the functions represented.

Inputs		All Possible Outputs
A	B	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
0	0	0	1	0	1	0	1	0	1	0	1	0	1	0	1	0	1
0	1	0	0	1	1	0	0	1	1	0	0	1	1	0	0	1	1
1	0	0	0	0	0	1	1	1	1	0	0	0	0	1	1	1	1
1	1	0	0	0	0	0	0	0	0	1	1	1	1	1	1	1	1

3. Complete the truth table and draw the schematic for the Boolean expression: F = A‾BC‾ + AC

A	B	C	F
0	0	0
0	0	1
0	1	0
0	1	1
1	0	0
1	0	1
1	1	0
1	1	1

4. (Adapted from Problem 8 from Digilent Real Digital Exercise 3)

The LA Angels of Anaheim stolen a base in 6 months, and the manager decided it was because the other teams were reading his signals to the base runners. He came up with a new set of signals (pulling on his EAR, lifting one LEG, patting the top of his HEAD, and BOWing) to indicate when runners should attempt to steal a base. A runner should STEAL a base if and only if the manager pulls his EAR and pats his HEAD while lifting his LEG, or if he BOWs and pats his HEAD without pulling his EAR, or anytime he pulls his EAR without lifting his LEG. Sketch a minimal circuit that could be used to indicate when a runner should steal a base.

5. Complete the following minterm/maxterm equations, and then write minimum Sum-of-Products (SOP) and Product-of-Sums (POS) equations for the logic system shown in the truth table.

A	B	C	F
0	0	0	1
0	0	1	0
0	1	0	0
0	1	1	1
1	0	0	0
1	0	1	1
1	1	0	1
1	1	1	0
FSOP =
FPOS =

F(A,B,C) = ∑ m ( )

F(A,B,C) = ∏ M ( )

6. Simplify the following Boolean expressions using Boolean algebra. Show all of your work. Then state how many inputs and gates are used.

1. Y = ABC‾ + AB + A‾BC‾
2. Z =(A+B‾)‾+ AB + (AC)‾

7. Find minimal SOP and POS Boolean expressions for the following system using the Karnaugh Map. Circle the simpler expression (if the SOP and POS expressions are equally simple, then circle both).

	CD
AB	00	01	11	10
	01	1	1	0
	11	0	0	0
	10	1	0	0

F_SOP =
F_POS =

Open response questions, there is no right or wrong answer

8. What is your major and what year are you into your degree (e.g. first year, second year, etc.) What area(s) or topic(s) are you interested in being involved with after you graduate? Please explain your response.

9. What topic(s) are you looking forward to learn more about in this class? What topic(s) would you like to see covered in this class? Please explain both of your responses.