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 D_{2}.
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 M_{2}.
5. Convert your M2 value to its equivalent 8-bit two's complement form. Let's call the result M_{2}C.
7. Now, using the values you've derived from given birth-date, evaluate the following expression, let's call the result R_{2}C:
R_{2}C = M_{2}C - D_{2}C
8. Convert your 8-bit R_{2}C value to back into its equivalent binary value. Let's call the result R_{2}.
9. Finally convert your binary R_{2} 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.