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In 1972, Intel's 8008 processor could execute 200,000 (200 thousand) instructions per second; at present, an Intel Core 2 processor can execute...
5. In 1972, Intel's 8008 processor could execute 200,000 (200 thousand) instructions per second; at present, an Intel Core 2 processor can execute 3,200,000,000 (3.2 billion) instructions per second. Let's assume that we program the 8008 to run a fastO(N Log2 N) sorting algorithm, and program the Core 2 to run a slowO(N2 )sorting algorithm. Assume the time to sort N values on the 8008 is 100/200,000 N Log2 N seconds; assume the time to sort N values on the Core 2 is 10/3,200,000,000 N2 seconds. Here the constant for fast sorting on the 8008 is 10 times as big as the constant for slow sorting on the Core 2 (both constants are divided by the speed of the machinesthe algorithm runs on).
a1) About how long does it take the 8008 to sort 1,000 values? ~
a2) About how long does it take the Core 2 to sort 1,000 values? ~
b1) About how long does it take the 8008 to sort 1,000,000 values? ~
b2) About how long does it take the Core 2 to sort 1,000,000 values? ~
c1) For what problem sizes Nis it faster to use the Core 2 for sorting?
c2) For what problem sizes N is it faster to use the 8008 for sorting?
In problems c1 and c2 only, compute your answer to the closest integer value (you can ignore decimal places). Use a calculator, spreadsheet, or a program to compute (possibly to guess and refine) your answer.
