Date: Tue, 05 Nov 1996 00:32:14 GMT Server: NCSA/1.5 Content-type: text/html Last-modified: Thu, 10 Oct 1996 20:02:36 GMT Content-length: 5639
Name (printed): |
Name (signed): |
Mohammad |
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Sridevi |
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Sunlung |
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(1) (4 points) Find the largest IEEE 32 bit floating point number that does not have an integer value. Express the answer in binary and in decimal.
ANSWER
all FPS numbers larger than: 100000000000000000000000.02 = 223 have integer values since the significant only holds 23 bits the next smaller FPS number is: 11111111111111111111111.12 = 223 - 0.5 = 8388607.510
(2) (2 points each, 6 points total) Write the hexadecimal values for x, y and z just after the following code executes:
ANSWER
move x, 0x0f0fc123 and x, x, 0xff00f000 # x = 0x0f00c000 not x, x # x = 0xf0ff3fff <- ans move y, 0x8f0aabc9 sll y, y, 5 # y = 0xe1557920 <- ans nor z, x, y # z = 0x0e008000 <- ans
(3) (3 points each, 6 points total) Do the following 2's complement multiplication. Indicate if either computation overflows for 12 bit words, for 6 bit words. Show your work. Check your results by redoing the computation in decimal.
001010 001010 x 111100 x 000011 -------- -------- ANSWER 111111111100 <- sign extend the -410 001010 <- 1010 x 1010 <- 1010 x 000011 <- 310 ------------ -------- 1111111111000 001010 111111111100 001010 ---------------- -------- 1001111111011000 <- 011000 is 2410 0011110 <- 011110 is 3010 in 6 bit, 2's comp in 6 bit, 2's comp 111111011000 is -40 in 12 bit 2's comp, no overflow in 12 or 6 bits no overflow for 12 bit words but overflow for 6 bit words
(4) (4 points) Show that the following two code segments give the same value for c, for any values of a and b. Hint: consider truth tables (see page 116 of the text).
and c, a, b not c, a not c not d, b or c, c, dANSWER
the first sequence is not(a and b) while the second is (not(a) or not(b)) column 4 and 7 of the following truth table are the same so not(a and b) is the same as not(a) or not(b) a b (a and b) not(a and b) not(a) not(b) (not(a) or not(b)) 0 0 0 1 1 1 1 0 1 0 1 1 0 1 1 0 0 1 0 1 1 1 1 1 0 0 0 0