Case Study $1$A

INSTRUCTIONS: Please attempt all questions, showing complete working to obtain full credit for the question. The assignment should be handwritten on paper and upon completion, submitted in class on the due date

Submit your assignment script with your NAME, ID# and COURCE CODE.

This Assessment is worth $10\%.$

DUE DATE: $6^{th}$ JUNE, $2024$

Convert $83\mathrm{.}0625$ to binary.

$(3$ marks$)$

Compute:

a$.{1101}_2{1010}_2$

$(2$ marks$)$

b$.{101101}_2{101}_2$

$(2$ marks$)$

Using $16-$bit computer representation, calculate $-6532+2965$

$(5$ marks$)$

Given the logical expression: not$(notpvvq)(qvvnotp).$

a$.$ Using the laws of logic, simplify the above logical expression.

$(5$ marks$)$

b$.$ Construct the truth table for the above logical expression.

$(5$ marks$)$

c$.$ State whether the logical expression is a Tautology, Contradiction or Contingency.

$(1$ mark$)$

Write the following argument in symbolic form.

'Either the fan is working or the fan is not plugged in$.$ The fan is working. Therefore, the fan is plugged in$.\text{'}$

$(2$ marks$)$