(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...

(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? (2+2+2+2=8 marks)
I.One's complement
II.Two's complement
III.Signed magnitude
IV.Unsigned magnitude

(b)Convert the followings: (7 marks)
I.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:

•Assignment component must pass (50 or above)
•Any 2 more assessments must pass
•Fail otherwise

Construct a truth table and find the minimized Boolean function. Draw a circuit diagram for the Boolean function.