Assignment : Data Representation & Digital Logic

Question 1

(a) Given a tiny computer that has a word size of 8 bits, what are the smallest negative numbers and the largest positive numbers that this computer can represent in each of the following representations?

I. One's complement

II. Two's complement

III. Signed magnitude

IV. Unsigned magnitude

(b) Convert the followings:

Please check Below correction in Assignment 1 - Question 1 (b):

Convert the followings:

1. 0x5AB into Octal

II. 101101.1012 into Decimal

III. 12348 into Binary

IV. 679810 into Base 5 number

V. 976.6310 into Binary

VI. 1001001011 into Hexadecimal

VII. 10011110 (8-bit 2's complement representation) to Decimal

Question 2

(a) Using basic Boolean algebra identities for Boolean variables X and Y, prove that X'(X+Y)+(XX+Y)(Y'+X)=Y+X. Please show all steps and mention the identities used. (6 marks)

(b) A subject has 4 assessments, such as Assignment, Blog, Discussion Forum and Quiz.

In order to pass in the subject, a student must get as below:

1. Assignment component must pass (50 or above)

2. Any 2 more assessments must pass

3. Fail otherwise

Construct a truth table and find the minimized Boolean function. Draw a circuit diagram for the Boolean function. (9 marks)

NOTE:

1. For Q2/b, you need to use any logic design simulator to draw the circuit. You have already two simulators are available in Logic design folder in interact resources. I think Logisim is very easy to use , and there is 3 minutes video showing how to use.

2. You need then to get ONE screen shot from designed circuit and paste it in your word document