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# Assignment 1: Data Representation & Digital Logic Due date: 24-Apr-2018 Return date: 01-May-2018 Submission method options Alternative submission method Task Total marks: 30 Answer the following...

Assignment 1: Data Representation & Digital Logic

Due date:24-Apr-2018

Return date:01-May-2018

Submission method options

Alternative submission method

Total marks: 30

Question 1

a) Determine the value of basexif (152)x= (6A)16 Please show all steps. [5 marks]

b) Convert the followings: (Please show all steps) [1.5x4=6 marks]

i) 0xBED into 3-base representation

ii) 3217into 2-base (binary) representation

iii) 1235 into octal representation

iv) 21.218into decimal representation

c) Given a (very) tiny computer that has a word size of 3 bits, what are the lowest value (negative number) and the highest value (positive number) that this computer can represent in each of the following representations? [2X3= 6 marks]

i) One's complement

ii) Two's complement

iii) Signed Magnitude

Question 2.

a) Are these two combinational circuits equivalent? Provide proof of your claim. [4 marks]

b)Consider the following logic diagram of a combinational circuit where A and B are inputs and X is the output. Two 2-input AND gates, one 2-input OR gate, and two inverters are used in the circuit. It is possible to reduce some of the logic gates without changing the functionality of the circuit. Such component reduction results in higher operating speed (less delay time from input signal transition to output signal transition), less power consumption, less cost, and greater reliability. Construct a logic diagram of a circuit which does have the same function output. Please show the steps. [4 marks]

c) Using basic Boolean algebra identities for Boolean variablesx, y, and z, prove that

Please show all steps and mention the identities used. [5 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;

Marking criteria

 Criteria HD (85%-100%) DI (75%-84%) CR (65%-74%) PS (50%-64%) FL (0%-49%) Comprehension of data representation and application of computer math calculations All calculations were correct. Appropriate mathematical symbols were used, and all steps/workings were shown. Almost all Calculations were correct except a minor error. Most of the calculations are correct. However, few steps were omitted. The methods used to solve the problem were correct, but there were one or two miscalculations. At least half of the calculations were correct. Some incorrect answers were the result of errors at some stage of the calculation, which propagated with the next steps. Some of the steps showed the basic understanding the numbering system. No attempt or most of the calculations were incorrect. Failed to show the steps of calculation. Either the answers were incorrect or the steps were wrong. Application of Boolean algebra and digital logic and interpretation of complex circuits The Boolean expressions are correct and minimised. All steps are explained. Correctly mentioned the Boolean identities. All identities were mentioned accurately. Boolean expressions and algebraic calculations were correct, however few steps were not shown or only minor error. Few minor error in applying the Boolean identities. Could reduce the number of logic gates, but not as much required by the question. More than half of the Boolean expressions were correct. Applied Boolean identities but could not reach to the final step. The Boolean equation, logic diagram and the truth tables were incorrect and they do not conform to the question.

Presentation

File naming convention: When you upload files to the TURNITIN for this subject, please use your student ID and Assignment number to name your files. For example, 123456_Assignment1.doc or 123456_Assignment1.docx etc (where XXXXXXXXXXis your Student ID)

Answered Same Day Apr 21, 2020

## Solution

Prateek answered on Apr 22 2020
Question 1.
a)  Determine the value of base x if (152)x = (6A)16    Please show all steps.   [5 marks]
(6A) in hex = 6*16 + 10 = 106 in decimal.
152 to base x can be represented as 1* x^2 + 5*x + 2
So the equality can be restated as :
x^2 + 5x + 2 = 106
=> x^2 + 5x -104=0
x=8 or x=-13
Considering the positive value for base x, x=8.
) Convert the followings: (Please show all steps) [1.5x4=6 marks]
i) 0xBED into 3-base representation
ii) 3217 into 2-base (binary) representation
iii) 1235 into octal representation
iv) 21.218 into decimal representation
i) 0xBED in decimal = 11*16*16 + 14*16 + 13
= 2816 + 224 + 13
= 3053
Converting to base 3 by repeated division:
3)3053 2
3)1017 0
3)339 0
3)113 2
3)37 1
3)12 0
3)4 1
1
Taking the remainders from bottom to top-
Solution: 11012002 in base 3
ii)
321 to base 7 = 3*7^2 + 2*7 + 1 = 147+14+1 = 162 to base 10.
Converting 162 to binary by repeated division by 2 and recording the rainder.
2) 162 0
2) 81 1
2) 40 0
2) 20 0
2) 10 0
2) 5 1
2) 2 0
1
Solution: 10100010 in binary.
iii) Converting 1235 to octal by repeated division:
8)1235 3
8)154 2
8)19 3
2
Solution: 2323 to base 8
iv) 21.21 base 8 to decimal:
Integer part: 2* 8 + 1 =...
SOLUTION.PDF