1. (1pts) What is the Hamming distance between these two bit patterns: and ?
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1 . (pts) What is the Hamming istance between these two bit patterns: 00 an 00? 2. (2pts) Write the equation for the carry out of the 4th aer cell in an ALU using carrylookahea, in terms of P s an G s. 3. (3pts) Given the choice between 8-bit carry lookahea an 8-bit carry lookahea with group size of 3 an ripple carry between groups, which is faster? Which is more expensive an why? 4. (5pts) What is the ifference between the Mealy an Moore moels of sequential esign? What is the avantage to the Moore approach? 5. (2pts) What is the ifference between a Flip-Flop an a latch? 6. (2 pts) What is a Karnaugh Map?
2 7. (0 pts) Assuming rising ege-triggere flipflops, what is the maximum clock frequency possible for the following circuit? (In other wors, what is the maximum clock frequency that will still guarantee correct behavior?) Use the following elay values, an assume all input signals become vali at time 0. (Tprop is the propagation time for the flipflop, the time it takes from the rising ege of the clock until the output of the FF is vali.) AND: 3ns NAND: 4ns NOT: 2ns MU: 5ns Tprop (DFF): 7ns Tsetup (DFF): 4ns Thol (DFF): 3ns Tprop (TFF): 9ns Tsetup (TFF): 2ns Thol (TFF): 2ns Y 0 TFF Q 0 TFF Q 0 DFF Q 0 DFF Q SEL Clock
3 8. (3pts) How far apart must vali coe wors be to allow Triple Error Detection (TED)? Quaruple Error Correction (QEC)? Quintuple (5) Error Correction sextuple (6) Error Detection (QECSED)? 9. (2 pts) Here is a2-bit Error Correction coe format (same one use in class): C C 3 C 2 C a. Given the ata bit pattern 0000 in a machine using the above ECC coe, what bit pattern gets sent to memory? (No creit will be given without work being shown.) b. In this same machine, the following bit pattern is retrieve from memory: Assuming the above Error Correction coe format, ientify an correct any errors that may have occurre uring transmission or storage. (No creit will be given without work being shown.)
4 0. (5 pts) You have erive the following karnaugh maps for the inputs to a JK flip-flop. Unfortunately, the parts epartment just calle an your company iscompletely out of JK flip-flops. All they have left in stock is T flip-flops, which you will have to use instea. Show the resulting karnaugh map for the moifie version of the circuit (the one that uses the T instea of the JK flip-flop.) Youonot have to write own the minimize equation. J K T
5 . (20) Given the following table, raw the Karnaugh maps for,, an an Z in terms of,, an, an then write minimum boolean equations for each. Present Next State Output State =0 = =0 = ( ) ( ) ( )
6 2. (5 pts) Given the following Karnaugh maps, implement the sequential machine using a JK FF for, an SR FF for, an a T FF for. Youonot nee to raw the gates, but you o nee to write own the minimize input equations for each of the inputs of each of the Flip Flops in the circuit.
7 3. (20 pts) The Presient of Freeonia, Rufus T. Firefly, has a sore back from carrying aroun all his money. Hewants to get one of those vibrating chairs he saw atthe mall, but he s too cheap to actually pay for one. Instea, he has hire you to moify his existing recliner an a the vibrating capability to it. Users have to pay, though, because he oesn t want his Prime Minister sneaking in an sitting in it constantly. Hewants the chair to accept two coins, the 0 Quatloo piece (the "imeloo") an the 30 Quatloo piece. Each 5-minute vibrating session costs 40 Quatloos. The chair must give change, because the Presient is a cheapskate. Let =30 Quatloo coin an 2=0 Quatloo coin, an assume both coins cannot be inserte simultaneously. Also assume that if you are stupi enough to put in 3 imeloos an then a 30 Quatloo piece, or two 30Quatloo pieces in a row, you will pay a 0 Quatloo penalty an only get imeloo back (because the Presient has the key to the change box on the chair anyway.) Draw the State Transistion Diagram (the circles an the arcs) for this finite state machine. Let S0=no money input (the Start state). Once you have a state transition iagram, minimize the number of states necessary an then assign bit patterns to each state an write own the corresponing state transition table. Assume you are using a Mealy moel. Label the transitions on the iagram using the format we use in class (inputs over outputs).
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