Answer the following questions: 1. Design a digital combinational circuit which compares two 2-bit.. 1 answer below »

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Answer the following questions:

1. Design a digital combinational circuit which compares two 2-bit binary numbers and produces results using a 2-bit binary number (please see the block diagram below). The output Z1Z0 depends on the inputs A1A0 and B1B0 according to the following criteria: If (A1A0 > B1B0) the output Z1Z0 = 10 If (A1A0 B1B0) the output Z1Z0 = 01 If (A1A0 = B1B0) the output Z1Z0 = 11

You should use minimum number of logic gates. [7 marks]

2. Using basic Boolean algebra identities, prove that ABC+ABC'+AB'C+A'BC = AB + AC + BC. Please show all steps and mention the identities used. [3 marks]

Rationale

This assessment task covers topic 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 use different identities of the Boolean algebra

Marking criteria

Questions

Fail (

Pass (50% – 64%)

Credit (65% – 74%)

Distinction (75% – 84%)

High Distinction (>84%) Question 1

The circuit design is incorrect and does not conform to the question.

Boolean expression is not correct, however the steps are correct. No or wrong circuit diagram.

The circuit design and the Boolean expression are correct but not minimised. Steps are correct. Minor mistakes in the Boolean algebra.

The circuit design is correct. The Boolean expression is minimised. All steps are explained. The circuit diagram is correct and neat.

Question 2

Neither the answers nor the steps are correct

Answer is not correct, but the steps are correct.

Answers are all correct but there are only few mistakes in the steps.

Answer s are all correct and complete. All steps are shown and identities are listed