# Final Exam -- Closed Book Section

10 May, 1994

The entire exam is to be turned in at 8:30 PM. Work the closed book section first and turn it in before you consult your books and notes to work on the open book section. The use of calculators is forbidden during the closed book section of the exam.

## Problem 1. (3 points)

Convert the decimal number 173 into a binary number.

## Problem 2. (3 points)

Convert the number -173 into a ten-bit two's complement binary number.

## Problem 3. (3 points)

Convert the unsigned binary number 100100110 into a decimal number.

## Problem 4. (3 points)

Convert the ten-bit two's complement number 1101110111 into a decimal number.

## Problem 5. (3 points)

What is the smallest number that can be stored in an eight-bit two's complement number?

## Problem 6. (3 points)

Draw the gate-level implementation of the Boolean function

• F(a, b, c) = a b' + c

using the standard representation of logic gates.

## Problem 7. (3 points)

Draw a truth table for the Boolean OR operation.

## Problem 8. (3 points)

Fill in the missing right hand sides of the following identities of DeMorgan's theorem:

• (x + y)' =
• (x y)' =

## Problem 9. (3 points)

What distinguishes a sequential circuit from a combinational circuit.

## Problem 10. (3 points)

Draw a high-level block diagram for 8x1 multiplexer showing all its inputs and outputs.

## Problem 11. (3 points)

What are the three states of a three state buffer?

## Problem 12. (3 points)

Why do most micro-programmed computers have at least two address registers?

## Problem 13. (3 points)

What is ``indirect address mode'' and why it is useful in computing array accesses?

## Problem 14. (1 point)

In what country did Lukasiewicz, the inventor of Polish notation, live?