Date: Tue, 05 Nov 1996 00:32:09 GMT Server: NCSA/1.5 Content-type: text/html Last-modified: Sat, 28 Sep 1996 19:29:11 GMT Content-length: 5230
Name (printed): |
Name (signed): |
Grader:
Mohammad |
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Sridevi |
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Sunlung |
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Total score:
(1, ver 1) (2 points) Convert 1113 to base 10.
ANSWER
(1, ver 2) (2 points) Convert 3339 to base 10.
ANSWER
(2, ver 1) (2 points) Convert 4510 to base 2.
ANSWER
45 rem 2 = 1 45 div 2 = 22 22 rem 2 = 0 22 div 2 = 11 11 rem 2 = 1 11 div 2 = 5 5 rem 2 = 1 5 div 2 = 2 2 rem 2 = 0 2 div 2 = 1 1 rem 2 = 1 1 div 2 = 0 so we get:
1011012
(2, ver 2) (5 points) Write -4510 as a 32 bit, 2's complement number.
ANSWER
45 rem 2 = 1 45 div 2 = 22 22 rem 2 = 0 22 div 2 = 11 11 rem 2 = 1 11 div 2 = 5 5 rem 2 = 1 5 div 2 = 2 2 rem 2 = 0 2 div 2 = 1 1 rem 2 = 1 1 div 2 = 0 so we get:
4510 = 1011012 pad to 32 bits: 0000 0000 0000 0000 0000 0000 0010 1101 flip bits: 1111 1111 1111 1111 1111 1111 1101 0010 add 1: 1111 1111 1111 1111 1111 1111 1101 0011 <- ans
(3, ver 1) (2 points) Convert fac16 to base 8.
ANSWER
fac16 = 1111 1010 11002 = 111 110 101 1002 = 76548
(3, ver 2) (2 points) Convert fca16 to base 8.
ANSWER
fca16 = 1111 1100 10102 = 111 100 111 0102 = 77128
(4, ver 1) (4 points) Convert 45.4062510 to base 2.
ANSWER
2 * .40625 = 0.8125 2 * .81250 = 1.625 2 * .62500 = 1.25 2 * .25000 = 0.5 2 * .50000 = 1.0 2 * .00000 = 0.0 so we get: 101101.011012
(4, ver 2) (5 points) Write 45.4062510 in IEEE FPS form.
ANSWER
45.4062510 = 101101.011012 = 1.0110101101 * 25 E = 510 + 12710 = 0111 11112 + 0000 01012 = 1000 01002 so we get: 0 1000 0100 01101011010000000000000 <- "S E F" form or: 0100 0010 0011 0101 1010 0000 0000 0000 = 0x4235a000 <- display form
(5, ver 1) (3 points) Consider an IEEE floating point representation where S is 1 bit, E is 4 bits and F is 7 bits. Write the largest positive floating point number in the 0x??? display notation.
ANSWER
ans: 0 1110 1111111 or: 0111 0111 1111 or: 0x77f
(5, ver 2) (3 points) Consider an IEEE floating point representation where S is 1 bit, E is 4 bits and F is 7 bits. Write the largest negative floating point number in the 0x??? display notation.
ANSWER
ans: 1 0001 0000000 is the float just to the left of 0.0 or: 1000 1000 0000 or: 0x880
(6, ver 1) (2 points each) What is the value of the bit pattern, 0000 0001 0100 0110, if it represents:
(a) a 16 bit unsigned binary integer?
ANSWER
(b) two ASCII characters?
ANSWER
ans: 0000 0001 = 116 = soh, 0100 0110 = 4616 = F
(6, ver 2) (3 points each) What is the value of the bit pattern, 1111 1111 1111 1110, if it represents:
(a) a 16 bit 2's complement integer?
ANSWER
the number is negative so, flip the bits: 0000 0000 0000 0001 add 1: 0000 0000 0000 0010 = 210 ans: -2
(b) a 16 bit sign magnitude integer (you may leave powers of 2 in your answer on this one)?
ANSWER
ans: - 111 1111 1111 11102 let x = 111 1111 1111 11102 so x + 2 = 1000 0000 0000 00002 = 215 ans: - (215 - 2)