1. Assume that we are doing single bit parity checking. (8)
a. Add a parity bit to give odd parity for each of the following:
b. Add a parity bit to give even parity for each of the following bytes:
2. Consider the 2 bit detect/1bit correct Hamming Code for four bit numbers using odd parity. What is the 7 bit word that should be used to describe the following numbers: (24)
3. For your answer to 2.b. above, change the bit in column 7. Show how the Hamming Code is used to correct that bit. (8)
4. For your answer to 2.b. above, change the bits in columns 2 and 5. (12)
a. Is the Hamming Code able to detect an error? Show your work.
b. Is the Hamming Code able to correct the error? Explain.
c. The Hamming Code indicated that a particular bit should be changed. Why did the Hamming Code suggest to fix that bit? What would then be true about the word if it was changed?
5. For a 16 bit data word. One of the groups will contain columns 4, 5, 6, 7, 12, 13, 14, 15, 20 and 21. (12)
a. Why were these particular columns put in the same group (hint: look at the binary values of the columns)? Show your work.
b. Why was column 17 not placed in this group?
c. How many parity bits are needed for a 16 bit word?
6. Draw the truth table for the following Boolean function: (8)
f (x, y) = x y
7. Draw the truth table for the following Boolean function: (8)
f (x, y) = x y
8. For the following reduction, two laws of Boolean logic were applied. What are they? (10)
a. x + x y x (1 + y)
b. Finish reducing the expression. Indicate the law you used.
9. Consider the following set of transistors with three inputs: (10)
Draw the truth table for the given gate (inputs are V1, V2 and V3 and the function result is Vout).