midterm1_sample3

midterm1_sample3 - UNIVERSITY OF CALIFORNIA LOS ANGELES...

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UNIVERSITY OF CALIFORNIA LOS ANGELES COMPUTER SCIENCE DEPARTMENT MIDTERM EXAMINATION - SOLUTIONS CS M51A Fall Quarter 2002 October 24, 2002

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MIDTERM SOLUTIONS CSM51A/EEM16 October 24, 2002 1 Find x, y, and z such that the following conditions are satis±ed: a) 67AE0F 16 = x 8 . b) 343 7 +241 6 = y 9 c) Find z 10 between 22 7 and 22 8 that in its binary representation has the largest number of 1’s. Solution: a) 67AE0F 16 = 0110 0111 1010 1110 0000 1111 2 = 011 001 111 010 111 000 001 111 2 = 31727017 8 x = 31727017 b) 343 7 =3 · 7 2 +4 · 7 1 +3 · 7 0 = 147 + 28 + 3 = 178 10 241 6 =2 · 6 2 · 6 1 +1 · 6 0 =72+24+1=97 10 343 7 6 = 178 10 +97 10 =275 10 275/9 = 30 5 30/9 = 3 3 3/9 = 0 3 275 10 = 335 9 y = 335 c) 22 7 =16 10 = 10000 2 22 8 =18 10 = 10010 2 The only number between (noninclusive) number between 22 7 and 22 8 is 17 10 = 10001 2 . Therefore z =17 10 . If we include both 22 7 and 22 8 into consideration, there is a tie between 17 10 and 18 10 (both have two 1s). 2
MIDTERM SOLUTIONS CSM51A/EEM16 October 24, 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 4 x 5 x 6 L=8 L=9 L=2 y 0 y 1 y 2 Solution: The number on the output of each gate represents its load. Propagation delays T pLH is shown inside of each gate. The critical path is indicated on the ±gure below x 1 x 0 x 2 x 3 x 4 x 5 x 6 L=8 L=9 L=2 y 0 y 1 y 2 .224 .224 .187 .187 .187 .196 .231 .234 2 2 3 3 1 1 1 .446 .542 The longest path: T pLH = 1.007ns 3

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MIDTERM SOLUTIONS CSM51A/EEM16 October 24, 2002 3 Among the following gates which ones are universal sets. (Provide complete proofs for each gate that you believe forms universal set.) xy x?y x ¯ y x y x y 00 0 0 1 0 01 0 1 1 0 10 1 1 0 1 11 0 1 1 1 Solution: = x y = 1 ?b =1 · b = b ; a?
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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_sample3 - UNIVERSITY OF CALIFORNIA LOS ANGELES...

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