Digital systems and microprocessors, Computer Engineering

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Your logic function for this assignment is to be derived from your own student number. The number 1224583 will be used as an example as to how you should derive your function and examples are given in brackets for this number. You should however use YOUR OWN NUMBER. If you do not then you will be awarded zero marks

Take your student number (1224583), and add your date of birth, using 2 digits for the day, 2 for the month and the last 2 digits of the year. If your birthday is 21st January 1993, then the number you should add, is 210193, giving you 1434776. If you do not wish to use your own birthday date, use a friend's. Place the different digits in ascending order (1, 3, 4, 6, 7). 

Add 5 to each of the individual digits of your ascending set (6, 8, 9, 11, 12,) and include any new numbers, starting from the highest    in your set of ascending numbers until you have a set of eight numbers. In this example you need three more numbers (9, 11, 12) to give the set              (1, 3, 4, 6, 7, 9, 11, 12,).

YOU need a set of EIGHT ascending numbers in the range 0 to 15. If your set still contains LESS than eight numbers, add 2 to the individual digits of your original ascending set, look for new digits, and continue until you have a set of eight numbers. This is the set of terms in the 1st canonical form of your function. In this example, the resulting 4-variabled function would be

                         F  =  f(ABCD)  = ∑(1, 3, 4, 6, 7,  9, 11, 12)

 

1. Write down the shorthand 1st canonical form equation of your own personal function derived as above.

2 Obtain the full 1st canonical form Boolean equation of your function in AND/OR/NOT form and draw its gate-level circuit diagram.

3 Obtain the shorthand equation of the 2nd canonical form of your function.

4 Obtain the full 2nd canonical form Boolean equation of your function in AND/OR/NOT form and draw its gate-level circuit diagram.

5 Enter your function on a fully labelled K-Map.

6 Obtain the minimal 1st canonical form (AND/OR/NOT)  of your function and draw its circuit diagram. (NOTE.  If at this point your personal function simplifies to a single variable or a single gate function, contact me and I will give you a more challenging function.)

7. Obtain the minimal 2nd canonical form (AND/OR/NOT) of your function and draw its circuit diagram.

8 . Use truth table equivalence to show that your minimal 1st and 2nd canonical forms do perform the same function.

9. Obtain the minimal NAND version of your function and draw its circuit diagram.

10. Obtain the minimal NOR version of your function and draw its circuit diagram.

11. Select at random, 4 terms NOT included in your original 1st canonical form shorthand equation in Question 1, to be don't care states. (NOTE: Once these don't cares have been defined they remain don't care inputs for questions 12, 13 and 14  of this assignment).  Obtain the minimal 1st canonical form (AND/OR/NOT)  using the original terms and, where appropriate, the don't care conditions. Draw the circuit diagram.

12. Obtain the minimal 2nd canonical form (AND/OR/NOT) using the original terms and where appropriate, the don't care conditions. Draw the circuit diagram.


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