Digital Logic and Boolean Algebra

The assignment consists of four tasks, covering topics such as decimal representation in binary and two's complement, IEEE-754 floating point representation, Boolean algebra and digital logic, and circuit design using a Logic Design simulator. The tasks require students to represent decimal numbers in different formats, analyze the representation of floating points in IEEE-754 format, solve Boolean algebra problems, and construct truth tables and minimize Boolean functions to design digital circuits.

 Task
1. Represent the following decimal numbers in both binary sign/magnitude and twos
complement using 16 bits: -29. [2 Marks]
2. A Computer uses IEEE-754 format to represent floating points. What value (in
decimal) the computer represents if the floating point is represented using the following
binary digits: [3 Marks]
0 01111110 10100000000000000000000
3. X’Y + XYZ’ + Y’ + XZ (Y+Y’) = 1 [2 marks]
4.Charles Sturt University (CSU) academic director want to select students in Sydney
Study Center to give them Gala Dinner Award. The recipient has completed three
subjects at least, two of them are core and the third is elective . Before he will select him,
he must check three subjects. He has come to the following conclusions [5 Marks =
2+1+2]:
· Give if two of core are High Distinction (HD) and elective subject is not.
· Give if one of the core subject and elective subject are HD.
· Don't hire otherwise.
Construct a truth table and find the minimized Boolean function to implement the logic
telling the director when to hire. Draw a circuit diagram for the Boolean function.

 Online submission via Turnitin is required for this assignment.
Rationale
This assessment task covers topic 2 and 3, and has been designed to ensure that you are
engaging with the subject content on a regular basis. More specifically it seeks to assess
your ability to:

 be able to apply Boolean algebra and digital logic to design and interpret digital
circuits.
 be able to use different identities of the Boolean algebra
 Marking criteria
Questions Fail (<50%) Pass (50% -
64%)
Credit (65% -
74%)
| Distinction
(75% - 84%)
High Distinction
(>84%)
Question 1 & 2 Neither the
answers are
correct nor the
steps.
Final answer is
correct without
showing the
process steps is
not accepted
The answer is not
correct, but the
steps are correct.
The answer is
correct or there
were only a few
slip of pen, or a
step or two were
missing.
Answer is correct
All steps were
shown.
The student should
submit the
solution has all
process steps.
Question 3 Neither the
answers nor the
steps are correct
Answer is not
correct, but the
steps are correct.
Answers are all
correct but there
are only few
mistakes in the
steps.
The efficiency has
not considered in
the solution
Answer s are all
correct and
complete. All
steps are shown
and identities are
listed.
The efficiency has
considered in the
solution
Question 4 The circuit design
is incorrect and
does not conform
to the question.
Boolean
expression is not
correct, however
the steps are
correct. No or
wrong circuit
The circuit design
and the Boolean
expression are
correct but not
minimised. Steps
are correct. Minor
The created truth
table is correct.
The circuit design
is correct. The
Boolean
expression is

Questions Fail (<50%) Pass (50% -
64%)
Credit (65% -
74%)
| Distinction
(75% - 84%)
High Distinction
(>84%)
diagram. mistakes in the
Boolean algebra.
The circuit hasn't
designed by using
Logic Design
simulator (Like
Cedar,
Logisim, ...etc)
minimised. All
steps are
explained. The
circuit diagram is
correct and neat.
The circuit
designed by using
Logic Design
simulator (Like
Cedar,
Logisim, ...etc)
Question 5 Neither the
answers nor the
steps are correct
Final answer is
correct without
showing the
process steps is
not accepted
Answer is not
correct, but the
steps are correct
Answers are all
correct but there
are only few
mistakes in the
steps.
Answers are all
correct and
complete. All
steps are shown
and identities are
listed
The student should
submit the
solution has all
process steps.