Write boolean expressions and construct the truth table

Question

Assignment: Data representation & Digital logic

Question 1

a) Determine the value of base x if (211)_x = (152)₈

b) A computer stores all integers in 8 bits. The computer also uses 2's complement method for representing negative numbers and IEEE 754 single precision representation for storing floating point values. Please show how the following values (in decimal) would be stored in the computer:

i) -35

ii) -22.625

Question 2:

a) Express the switching circuit shown in the figure below in binary logic notation:

b) Write Boolean expressions and construct the truth table describing the outputs of the circuit depicted by the following logic diagram:

c) Using basic Boolean algebra identities for Boolean variables A, B and C, prove that ABC+ ABC' + AB'C + A'BC = AB + AC + BC. Please show all steps and mention the identities used.

Guidelines for Q1b: A computer stores all integers in 8 bits. The computer also uses 2's complement method for representing negative numbers and IEEE 754 single precision representation for storing floating point values. Please show how the following values (in decimal) would be stored in the computer

i) -35 ii) -22.625

Clarification

It means you need to use 2's Complement for -35, and use IEEE Single Precision for -22.625.

NOTE:
For -35, you need to convert it first to sign magnitude, THEN to 1's Complements, and then to 2's complement. Important Note: Kindly properly solve the questions writing each steps.