Task 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...

Task
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: [6 marks]

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. [9 marks]

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. [6 marks]

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;