CPSC 2105 Introduction to Computer Organization
Take-Home Midterm Due at 1:00 PM on Monday March 13, 2006
SHOW ALL OF YOUR WORK.
NO CREDIT GIVEN FOR ANSWERS THAT SHOW NO WORK.
DO NOT PLACE ANY WORK ON THIS SHEET.
1. (10 points) What is the range of integers that can be represented in 12 binary bits
a) if the integers are stored as unsigned numbers?
b) if the integers are stored as two’s–complement signed numbers?
2. (10 points) Convert the following decimal integers to 12–bit two’s–complement form.
Show your work as most calculator will do this automatically.
a) 1023 b) – 1984
3. (10 points) Using eight hexadecimal digits, show the IEEE–754 Single–Precision
representation of the decimal number – 0.03125 (It is negative).
4. (10 points) Using eight hexadecimal digits, show the IEEE–754 Single–Precision
representation of the decimal number 16.75.
5. (10 points) Using eight hexadecimal digits, show the ASCII code representation of
the four–character string “1024”. Hint: This only looks like a number.
6. (10 points) Use a number of two–input OR Gates to fabricate a four–input OR.
Put another way, use only two–input OR gates (page 102 of the text) to
draw a circuit diagram for the logical function F(W, X, Y, Z) = W+X+Y+Z.
7. (10 points) Using a truth–table, prove or disprove (X Y) Z = X (Y Z).
8. (10 points) Consider the following truth table, which purports to represent a Boolean
function of two Boolean variables: X and Z. It has been written with 8
columns and 3 Boolean variables, X, Y, and Z. Rewrite this as an
equivalent four–row truth table.
X Y Z F(X, Z)
0 0 0 0
0 0 1 1
0 1 0 0
0 1 1 1
1 0 0 1
1 0 1 0
1 1 0 1
1 1 1 0
9. (10 points) How many rows are in the truth table for the Boolean function
F(U, V, X, Y, Z), where all variables are Boolean?
10. (10 points) Convert the hexadecimal number 0xCAFE as an unsigned number.
a) Convert this to a decimal number. It will be positive.
b) Convert this to a binary number. It will have 16 bits.