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# hw10_SLN - ECE 211 HW 10 SOLUTIONS p 1 of 16

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ECE 211 HW 10 SOLUTIONS p 1 of 16 /var/www/apps/collegelist/repos/collegelist/trunk/collegelist/tmp/scratch2/5254087.doc HW Set 10 – SOLUTIONS 1. Let t p denote the propagation delay time of the PAL. (The propagation delay time is the time it takes for a signal to go through the chip, from input pins to output pin.) (a) In lecture we realized Q = Σ 18 products using 3 output pins. In terms of t p , what is the delay time from the inputs to Q? (b) Can you realize Q such that you obtain a shorter delay? If 'yes', clearly explain your answer and include a circuit diagram showing how use use the PAL. Solution: (a) The delay to Q8 is t p . We go through the chip again to obtain Q15; the delay to Q15 is 2 t p . We go through the chip a third time to obtain Q; the delay to Q15 is 3 t p . Redrawn, to emphasize the propagation delay:

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ECE 211 HW 10 SOLUTIONS p 2 of 16 (b) Yes. We can realize a sum of 8 products on one pin; call the output Q1. We can realize a sum of another 8 products on another pin; call its output Q2. With a third pin, we realize Q1 + Q2 + Σ 2 products. The delay to Q1 is t p , the delay to Q2 is also t p . The delay to Q is 2 t p . [ The same circuit, redrawn: ]
ECE 211 HW 10 SOLUTIONS p 3 of 16 2. Using one 18P8 PAL, realize two functions F, G where F = Σ 36 products G = Σ 22 products F, G are functions of the same ten variables. (a) Complete the table to show how you are using the 18P8. (b) State the propagation delay ( in terms of t p – see Problem 1 for the definition of t p ) from the inputs to F, to G. (c) Are your delay times the smallest they can be? If you can make them smaller, please explain how you will do it. Solution: (a) (b) One approach is to build up the number of products: F8 = Σ 8 products F15 = F8 + Σ 7 products = Σ 15 products F22 = F15 + Σ 7 products = Σ 22 products F29 = F22 + Σ 7 products = Σ 29 products F = F29 + Σ 7 products = Σ 36 products We use 5 pins for realizing F. We realize G with a similar approach: G8 = Σ 8 products G15 = G8 + Σ 7 products = Σ 15 products G = G15 + Σ 7 products = Σ 22 products We use 3 pins for realizing F. The table is:

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ECE 211 HW 10 SOLUTIONS p 4 of 16 (Problem 2) 18P8 Table, including propagation delay times for each output. Pin Mode Signal Name Number of Products Used Input (Input) IN1 N/A Input (Input) IN2 N/A Input (Input) IN3 N/A Input (Input) IN4 N/A Input (Input) IN5 N/A Input (Input) IN6 N/A Input (Input) IN7 N/A Input (Input) IN8 N/A Input (Input) IN9 N/A Input (Input) IN10 N/A Bidirectional Output F8 8 tp Bidirectional Output F15 8 2 tp Bidirectional Output F22 8 3 tp Bidirectional Output F29 8 4 tp Bidirectional Output F 8 5 tp Bidirectional Output G8 8 tp Bidirectional Output G15 8 2 tp Bidirectional Output G 8 3 tp Circuit: (Next page)
ECE 211 HW 10 SOLUTIONS p 5 of 16 (2.)

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## This homework help was uploaded on 04/17/2008 for the course ECE 211 taught by Professor Nestor during the Fall '07 term at Lafayette.

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hw10_SLN - ECE 211 HW 10 SOLUTIONS p 1 of 16

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