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EE141_HW9_sol

# EE141_HW9_sol - UNIVERSITY OF CALIFORNIA BERKELEY College...

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UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Department of Electrical Engineering and Computer Sciences Elad Alon Homework #9 EECS141 PROBLEM 1: LOGIC STYLES Problems 3)b) and 3)c) from the EE141 Fall07 Midterm #2 (available on the web) Solution: See solutions posted on the web. PROBLEM 2: FLIP-FLOP TIMING Problem #4 from the EE141 Fall08 Final (available on the web). Solution: See solutions posted on the web. PROBLEM 3: “PULSED” LATCH TIMING Consider the simple state machine shown above. A, B, and C represent combinational logic blocks with the following properties: t logic ,minA = 200 ps; t logic, maxA = 1 ns; t logic, minB = 300 ps; t logic, maxB = 2 ns; t logic, minC = 100 ps; t logic, maxC = 0.5 ns; The L-units represent positive latches clocked by φ (i.e., the latches are transparent when φ is high). These latches have a setup time of 150 ps and a t d-q delay of 250 ps (when the

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latch is transparent). The clock to output delay t clk-q is 100 ps, and t hold is 100 ps. The clock φ has a period T clk and is high for a duration of T on – in other words, the duty cycle of the clock is T on / T clk . a) Determine the conditions on the clock necessary to avoid the occurrence of hold- time violations. Solution: We want to ensure that there is no way for a new value at the output of a latch to race through the logic so quickly that the value of the latch changes again before the clock goes low. There are two possible paths for this to happen: L1 Æ A Æ C Æ L2, and L2 Æ B Æ C Æ L2; since t logic,minA is less than t logic,minB , the first of these two paths is the most critical one. Therefore, the maximum T on we can use is set by: t clk-q + t logic,minA + t logic,minC > T on + t hold T on
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EE141_HW9_sol - UNIVERSITY OF CALIFORNIA BERKELEY College...

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