midterm1_sample2

midterm1_sample2 - UNIVERSITY OF CALIFORNIA LOS ANGELES...

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UNIVERSITY OF CALIFORNIA LOS ANGELES COMPUTER SCIENCE DEPARTMENT MIDTERM EXAMINATION - SOLUTIONS CS M51A Winter Quarter 2003 February 3, 2002
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MIDTERM SOLUTIONS CSM51A/EEM16 February 5, 2002 1 Find x, y, and z such that the following conditions are satis±ed: a) B4AC5D79 16 = x 8 . b) 208 11 = y 7 c) Find z 4 , which is larger than 44 4 andissma l lerthan44 11 , that has the largest sum of digits. Solution: a) B4AC5D79 16 = 1011 0100 1010 1100 0101 1101 0111 1001 2 = 010 110 100 101 011 000 101 110 101 111 001 2 = 26453056571 8 x = 26453056571 b) 208 11 = y 7 208 11 =2 · 11 2 +0 · 11 1 +8 · 11 0 = 242 + 0 + 8 = 25010 250/7 = 35 5 35/7 = 5 0 5/7 = 0 5 250 10 = 505 7 y = 505 c) Find z 4 , which is larger than 44 5 and is smaller than 44 11 , that has the largest sum of digits. 44 5 =44 5 =4 · 5 1 +4 · 5 0 =20+4=24 10 24/4 = 6 0 6/4 = 1 2 1/4 = 0 1 44 5 =24 10 =120 4 44 11 11 · 11 1 · 11 0 =44+4=48 10 48/4 = 12 0 12/4 = 3 0 3/4 = 0 3 44 11 =48 10 = 300 4 The number with the largest sum of digits between 120 4 and 300 4 is 233 4 . z =233 Page 2 of 6
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MIDTERM SOLUTIONS CSM51A/EEM16 February 5, 2002 2 Find the critical path and its length for the following gate network. Consider only LH delays for all gates. x 1 x 0 x 2 x 3 x 5 x 6 L=6 L=3 L=5 y 0 y 2 y 3 L=4 y 1 x 4 x 7 x 8 x 6 Solution: Gate A: 2-input NAND gate, Load = 3 0.05+0.038L = 0.05+0.034(3) = 0.164 Gate B: 3-input AND gate, Load = 3 0.20+0.038L = 0.20+0.038(3) = 0.314 Gate D: NOT gate, Load = 1 0.02+0.038L = 0.02+0.038(1) = 0.058 Gate C: 3-input NOR gate, Load = 2 0.16+0.111L = 0.06+0.111(2) = 0.382 Input to C: D, 0.058 0.382+0.058 = 0.440 Gate E: 4-input OR gate, Load = 1 0.13+0.038L = 0.13+0.038(1) = 0.168 Input to E: A, 0.164 0.168+0.164 = 0.332 Gate F: NOT gate, Load = 2 0.02+0.038L = 0.02+0.038(2) = 0.096
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This note was uploaded on 10/07/2011 for the course CS m51 taught by Professor Staff during the Spring '11 term at UCLA.

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midterm1_sample2 - UNIVERSITY OF CALIFORNIA LOS ANGELES...

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