BINARY NUMBERS AND THEIR DECIMAL EQUIVALENTS THAT ARE REPRESENTABLE

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BINARY NUMBERS AND THEIR DECIMAL EQUIVALENTS THAT ARE REPRESENTABLE

1. Using a "word" of 5 bits, list all of the possible signed binary numbers and their decimal equivalents that are representable in: [6 marks]
 
a. Magnitude
b. One`s complement
c. Two`s complement
 
2. Express the (- 1/32) number in IEEE 32-bit floating-point format. [5 marks]
 
3. Using Boolean algebra, prove that: [3 marks]
 
X’Y + XYZ’ + Y’ + XZ (Y+Y’) = 1

4. Charles Sturt University (CSU) is conducting three sessions every year. The BEGIN month for Session 1 is March, and it end is Jun. SESSION 2 BEGINS in July, and it end is October. SESSION 3 BEGINS in November, and it end is February.
 
Write a Boolean function and design a logic circuit, use of basic logic gates to activate these three sessions for CSU. Design a circuit with four inputs (A, B, C, and D) representing the bits in a binary number, and three outputs (S1_Active, S2_Active, and S3_Active). [6marks]
 
When the input is session 1, the output S1_Active should be one and all other outputs should be zero
 
5. Complete the truth table for the following sequential circuit: [5 marks]



Online submission via Turnitin is required for this assignment.
 
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 Boolean algebra and digital logic to design and interpret digital circuits.
• be able to describe the concepts of data representations and use appropriate methods of implementation;