1. How many orders of magnitude larger than 520 is 40,000? The nearest power of ten to 520 is 1,000, and the nearest power of ten to 40,000 is 10,000, so 40,000 is just one order of magnitude larger than 520. 2. How many orders of magnitude larger than 520 is 90,000? The nearest power of ten to 90,000 is 100,000, so 90,000 is two orders of magnitude larger than 520. 3. How many orders of magnitude larger than a picosecond is a millisecond? A picosecond is 10^-12; a millisecond is 10^-3, so a millisecond is 12-3=9 orders of magnitude larger than a picosecond. 4. Convert 250 nanoseconds to picoseconds. 250,000 picoseconds 5. Convert 250 nanoseconds to microseconds. 0.250 microseconds 6. Convert 250 milliseconds to nanoseconds. 250,000,000 nanoseconds 7. What is the “normal” representation of 5,280µsec? 5.280 msec. 8. On the average, how many yes/no questions would you have to ask someone if they were thinking of a number between 1 and 10? log2(10) = ln(10) / ln(2) = 3.322 9. How many bits would you need to encode the digits 0 … 9? ceil(log2(10)) = 4 10. Write out two different binary codes to represent the digits 0 … 9. BCD Gray 0 0000 0000 1 0001 0001 2 0010 0011 3 0011 0010 4 0100 0110 5 0101 0111 6 0110 0101 7 0111 0100 8 1000 1100 9 1001 1101 * 1010 1111 * 1011 1110 * 1100 1010 * 1101 1011 * 1110 1001 * 1111 1000 * = unused code values Gray code: only 1 bit differs between adjacent values. 11. Calculate the weighted average of the following values; show all work: Value Frequency 70 200 80 100 90 700 Divide each frequency by 1000, and their sum is 1.0, so 70×.2 + 80×.1 + 90×.7 = 85 12. At Queens College, grade point averages use the number of credits for each letter grade as the weights and the following table to relate letter grades to values: Grade Value A+ 4.0 A 4.0 A- 3.7 B+ 3.3 B 3.0 B- 2.7 C+ 2.3 C 2.0 C- 1.7 D+ 1.3 D 1.0 F 0.0 What is the GPA of a student who has received A- in 3 courses, B+ in 2 courses, and B in 5 courses, if each course was 3 credits? Show all work. 9×3.7 + 6×3.3 + 15×3.0 = 98.1 98.1 /(9+6+15) = 3.270 13. What would be the GPA of the student in the previous question if he had failed a 1-credit course in addition to receiving the grades listed in the question? 98.1/(9+6+15+1) = 3.164 14. Show the terms needed to calculate how many bits would be needed to record 10 sec of CD-quality music (stereo). That is, do not do the calculation, but show what numbers would be multiplied together to get the answer. 44,000 samples per second × 10 seconds × 2 channels × 12 bits per channel 15. How many bits in 64 KB? Show all work. 64 = 2^6 K = 2^10 B = 2^3 64KB = 2^19 bits = 524,288 bits 16. A disk spins at 10,000 RPM. How long does it take to make one revolution? Answer in seconds, using the correct unit of measure to give a “normal” value with the integer part between 1 and 999. 10,000 RPM / 60 = 166.667 RPS (revolutions per second) = 0.006 seconds per revolution = 6 msec. 17. How long would it take to transfer a 250 MB program from disk to main memory if the initial latency is 5 msec and the bandwidth of the channel between the disk and main memory is 600 Mbps? Show all work. 250 MB = 2000 Mb 2000Mb/600Mbs = 3.333 sec transfer time + 0.005 sec latency ------- 3.338 sec 18. How long would it take to execute one million instructions if the average number of clock cycles per instruction is 2.2 and the clock speed is 3 GHz? Show all work. sec/program = instructions/program × clocks/instruction × seconds/clock = 10^6 × 2.2 × 1/3 × 10^-9 = 0.0007333 sec = 733.3 microseconds 19. “Computer A is twice as fast as computer B.” What does that mean in terms of how long it takes the two computers to execute a program? Computer A requires half as much time to execute the program compared to Computer b. 20. “Computer A is 100% slower than Computer B.” Turn that into a meaningful statement, if you can. If you cannot, explain why not. My best guess would be to interpret "is 100% slower" to mean "requires 100% more time." 100% more time would mean twice as much time, so Computer A is apparently half as fast as Computer B. But that's just a guess. When comparing ratios, it makes more sense to talk about the ratio of the slower time divided by the longer time, and it is ambiguous what the times involved in a "times slower" sentence mean.