Data Representation & Digital Logic

Question 1
a) A Computer uses IEEE-75a single precision format to represent floating points. What value (in decimal) the computer
represents ifthe floating point is represented using the following binary digits: [6 marks]
0 0111111 0 1 01 OOOOOOOOOOOOOOOOOOOO
b) Using a “word” of5 bits, list all ofthe 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 during1:00 pm – 61:00 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]