Boolean logic-truth table and digital circuit diagram, Algebra

Part A. relates to data representation and Part B. relates to Boolean logic. 

Part A. Data Representation

The very first thing you need to do to begin Part A is to make sure that your work report clearly states this (05.08.1989) birth-date in dd/mm/yyyy format.

To complete the rest of Part A you need to apply the following operations to the specified digits from this (05.08.1989) birth-date.

1.  Take the two 'dd' digits from given birth-date and simply add 15 to them. Let's call the result of this base 10 addition D10.

2.  Convert your D10 value to its equivalent 8-bit binary representation. Let's call the result D2.

3.  Now take the two 'mm' digits from given birth-date and simply add 2 to them. Let's call the result of this base 10 addition M10.

4.  Convert your M10 value to its equivalent 8-bit binary representation. Let's call the result M2.

5.  Convert your M2 value to its equivalent 8-bit two's complement form. Let's call the result M2C.

7.  Now, using the values you've derived from given birth-date, evaluate the following expression, let's call the result R2C:

R2C = M2C - D2C

8.  Convert your 8-bit R2C value to back into its equivalent binary value. Let's call the result R2.

9.  Finally convert your binary R2 value back into its equivalent base 10 form. Let's call the result R10.

In your work report for Part A you should clearly show all of your working-out for each of the above steps and, where appropriate, write a brief description of what your working-out shows.

Part B. Boolean Logic

Consider the following scenario:

Some of the progression regulations that are applied in our university Exam Boards to determine whether a student is allowed to progress from level II (second-year) of their degree studies to start level III (third-year) of their degree are as follows:

"In order to proceed to Level III, current Level II students must:

(a) not be carrying forward ANY failed level 1 modules, and

(b) be carrying forward less than TWO failed Level II modules."

(Note: the progression rules take no account of whether module pass marks were attained by way of a first-sit or made good via re-sits etc. so those complexities can be ignored).

For this part you should provide complete answers for the following tasks, based upon the above scenario:

1.  Draw a truth table that summarizes every possible combination of progression conditions (a) and (b) and for each combination shows whether progression is allowed or not.

2.    Draw a simple digital circuit diagram that implements the logic of your progression truth table. (Such a logic circuit could be used to red-flag certain student records when they are being processed for the exam boards etc.) HINT: only simple combinations of

AND and NOT gates should be required for this digital circuit.

Posted Date: 2/28/2013 2:03:00 AM | Location : United States







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