# All questions are 20 pts each. Answer all 5 questions.

All questions are 20 pts each. Answer all 5 questions. Show/explain your work. Short answers cannot get full points! Cite your sources or you will lose points, or more, for copy-paste answers.
Q1. Convert 1.375 and 0.75 to the 14-bit floating point format of the textbook and add them up in that format, then convert your 14-bit result back to decimal and verify your computation.
Q2. What is the smallest 32-bit floating point number f such that 128 + f 128 ?
What is the smallest 32-bit floating point number g such that 1 + g 1 ?
What is the relationship between f and g?
A. Where f and g are differentiable functions. We have found that the given functions have the same derivative. In general, if two differentiable functions differs by a constant at x, its derivatives slopes at this point are the same.
Write a short C++ or Python program to support your answer (for example, show that you checked whether there is no smaller number than your f by trying 128+f/2 == 128.
Q3. Explain what changes are needed to change the 4×3 memory presented on Slide 62 of Chapter 3 to a 16×6 memory.
Q4. Complete the characteristic table for the sequential circuit shown below.
# x A Next State
A
1 0 0 ?
2 0 1 ?
3 1 0 ?
4 1 1 ?
AUM Computer Architecture Quiz 2
There are two questions (Q1 and Q2). Each question is 50 pts. Answer both questions.
Q1. The logic circuit shown in the diagram directly implements which of the Boolean expressions given below?

A) (x + y)z(xy)
B) (xy)+ z(x + y)
C) (x + y)z(xy)
D) (xy)+ z(x + y)
Label the outputs of gates to show intermediate results.
Q2. Undergraduate Students only: Use logicly to build a 3-bit adder/subtractor for 2’s complement numbers. Use a hex-display to show your sum. Using 3 bits limit our range to -4 to +3. Do not worry about overflows. For example 3+2 will be overflow but we do not care about those cases. Here is what we care about, for example: One addend is -1 (represented by “111” of course) and the other addend is -2 (represented by “110”) then the sum is -3 (“101”) and the hex display will show 5. That’s because as we said in class, there is no -3, there is 8-3 = 5. If we add 1 and 2, we should get 3 displayed on the hex display.
Q2. Graduate Students only: Use logicly to complete the following. Hamming code to hex-display: Suppose we have 4-bit data and 3 check bits for Hamming code as shown below. Develop a logic circuit to display corrected data on a hex display.
7-bit hamming input received is 1010001.
So, data bits received are 1010 (shown as A on the top hex display) but checking the parity bits we have the following:
Bit-1 Bit-3 Bit-5 Bit-7 have 3 -one-s, so Bit-1 has error.
Bit-2 Bit-3 Bit-6 Bit-7 have 1 -one-, so Bit-2 has error.
Bit-4 Bit-5 Bit-6 Bit-7 have 2 -one-s, so Bit-4 has no error.
Bit-3 must have error.
The corrected data should be 1011.
So the hex-display of the circuit receiving this 7-bit code should display B on the bottom hex display.
In your submission submit two different screenshots of input-output of course also showing the logic circuit. Do not show the A?B example I showed above, find two other cases. Also add your name (as I added mine in the middle) using a label from Logicly.

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