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Posted: April 22nd, 2020

# Assessment item – Data Representation & Digital Logic TASK

Assessment item – Data Representation & Digital Logic
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… × 2exp). 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

Criteria HD
Comprehension of concepts of data representation
7 Marks Implements appropriate mathematical methods to arrive at correct answers. Shows all steps and all calculations are accurate.
Development of a Boolean expression and logic circuit from truth table
4 Marks Sum of Products expression is correct.
Logisim circuit correctly implements the Boolean expression.
Simplification of Boolean expression using laws of Boolean algebra
4 marks Simplification is correct showing all steps and correctly identifies all the Boolean laws used.

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