Assignment 1: Data Representation & Digital

Question 1

a) A Computer uses IEEE-754 single precision format to represent floating points. What value (in decimal) the computer represents if the floating point is represented using the following binary digits:

0 01111110 10100000000000000000000

b) Using a "word" of 5 bits, list all of the possible signed binary numbers and their decimal equivalents that are represent able in: [3+3+3 = 9 marks]
i. Signed magnitude
ii. One's complement
iii. Two's complement

Question 2

a) Write a Boolean function and construct a logic diagram of a circuit which use of basic logic gates to activate CSU main entrance door during 9:00 am to 12:00 pm and after lunch time during 1:00 pm - 4:00 pm. You need to use 24 hour clock timing when designing this circuit.

Please insert the Boolean expression, minimisation, and the diagram

b) Using basic Boolean algebra identities for Boolean variables A, B and C, prove that X'Y + XYZ' + Y' + XZ (Y+Y') = 1. Please show all steps and mention the identities used.

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 an understanding of data representations and calculations to practical situations;
- be able to apply Boolean algebra and digital logic to design and interpret complex digital circuits;