Final exam for CSCI 274

This is an open book, open notes exam; however, the use of calculators is forbidden. The exam is to be turned in by 8:30 PM.

Problem 1. (10 points)

Convert the following decimal numbers into 10-bit two's-complement binary numbers

Problem 2. (10 points)

Represent the following 10-bit two's-complement numbers as decimal numbers

Problem 3. (10 points)

Convert the decimal number 6.65 into a floating point number with one sign bit, an eight-bit exponent expressed using excess-127 notation, and a 23-bit mantissa. By the way, if it takes you a long time to derive the mantissa, you are doing something wrong.

Problem 4. (10 points)

Use either a truth table or Boolean algebra to show that the following two Boolean expressions are equivalent:

Problem 5. (10 points)

Draw a sum-of-products circuit implementation of the following Boolean expression

Problem 6. (10 points)

Now implement the Boolean expression, ( x + y ) z', of the previous problem using only four two-input NAND gates. Hint: Start with the sum-of-products implementation.

Problem 7. (10 points)

If registers A and B have the following values:

what are the values of the following five expressions

A + B + is ordinary addition
A - B - is ordinary addition
A AND B AND is bit-wise logical and,
C's & operator, the upside-down V
asl B asl is arithmetic shift left
csl B csl is circular shift left

Problem 8. (10 points)

Look at Figure 5-4 on page 130 of the textbook, if

what happens in the next bus transaction?

Problem 9. (10 points)

How would you set the control inputs of the bus system shown in Figure 5-4 on page 130 of the textbook to execute the following RTL statement?

Problem 10. (10 points)

Suppose the following 16 bit hexadecimal values are stored in the memory of the "basic computer" described in Table 5-2 on page 133 of the textbook.

What action is performed when these five words are executed in order?