Data Representation & Digital Logic

Assessment
item – Data Representation & Digital Logic

Task

Overview

This
assessment consists of two questions. The first one looks into how
computers represent data and how we can interconvert these
representations. The second question looks at finding a Boolean
expression for an output variable given a truth table and then
drawing a logic circuit diagram using a simulator and testing for
errors.

Question
1 – Data Representation in Computer [3 + 4 marks]

(a)
Using
the rules of overflow, prove that adding -107 and -40 is not possible
in an 8-bit computer using 2’s complement integers. Show all
workings.

(b)
A
16-bit floating point representation is defined like this: 1 bit for
sign, 6 bits for exponent and 9 bits for significand. Floating point
number must be normalized (in the form 0.1… × 2^exp).
Exponent is stored in one’s complement representation. Significand
is stored as is without any hidden bits. Find out the smallest
positive number that can be stored in such a system. Work out its (i)
16 bit binary (ii) equivalent base 10 number in scientific notation.
Show all workings. 

Important:
For both questions, ZERO marks will be awarded if all mathematical
workings are not shown.

Question
2 – Boolean Algebra and Circuits [2 + 2 + 4 marks]

(a)
Given
the truth table below, find out a Boolean expression for output
variable Z in the canonical sum of products form.

(b)
For
the original (non-simplified) Boolean expression derived in part (a),
draw a logic circuit diagram using the ‘Logisim Evolution’
simulator. Submit the screenshot of completed circuit, as well as the
Logisim file as part of the assignment, as described later.
Hand-drawn diagrams will not be accepted. Make sure you test all the
16 combinations from the truth table to ensure there are no errors in
the circuit.

Click
here to download Logisim Evolution.
Do not get it from external sources. Before you can run it, you must
have Java installed on your computer. If required, you can get it
from Java.com.

For
guidance on how to use Logisim, watch
this demo video.

(c)
Simplify the Boolean expression from part (a) using the laws of
Boolean algebra. Show all the simplification steps and name the law
used for simplification at each step.

Submission
Format

Your
submission should include a pdf document containing answer to both
questions.  Secondly you need to provide the logisim file for Q2
(b). Compress both files into a ZIP archive and upload the zip file
to TURNITIN.

Rationale

This
assessment task will assess the following learning outcome/s:

• be
  able to define and appropriately use computer systems terminologies.

• be
  able to describe the concepts of data representations and use
  appropriate methods of implementation.

• be
  able to apply Boolean algebra and digital logic to understand
  computer operation.

This
assessment item covers topics 1, 2 and 3. It has been designed to
ensure that you are engaging with the subject content on a regular
basis.

Marking
criteria and standards

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