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hw3aSol - 1 CSE 260 — Digital Computers Organization and...

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Unformatted text preview: 1. CSE 260 — Digital Computers: Organization and Logical Design Homework 6 Solutions [on Turner (10 points) Show that the exclusive-or function is associative. That is, AEB(B€BC)=(A®B)€9C. You can do this using a truth table. Based on this, give a circuit using 2 input xor gates that computes the odd function on eight inputs. If each xor gate is implemented using NAND gates (as shown on page 3- 8 of the lecture notes) what is the worst-case delay for your circuit? (mung. ius {per MAJJD) odd Cfuud'i‘am M % :“Fws , 3 at; M :5 , :3)?" flDL 2)»? fl K3 overall Ada} D‘ 2. (10 points) Consider a CMOS inverter that drives one other gate and assume that the propagation delay for a high-to-low transition at the inverter output is 1 ns. Now suppose we replace the inverter with a 2 input NAND gate constructed using transistors that are the same as those used in the inverter. What is the time for a high-to-low transition at the output of the NAND gate? Explain why. What if the 2 input NAND is replaced with a three input NAND? \ +2!" I w) 5' {émfit ta Madonna wig? rutgi'moaz MW twrud on my!) Z 19de K5 wakw {Va neat sthui P. WW Fug/“mi 8K Mersey; rwtgtmuae. «(ZR Mil/U1) mm? discharge: aui’pui’ {ZA’FQC (“tan/La! Wrousfzc rasistautce Wig "FLUFQQ, are large, 30> Jc—F'wuL ear sta‘i‘w {4: ZV‘S, Fav- 3 TMPD& MAME) Hwy. 7:4 EMS 3. (10 points) Consider a circuit with 12 inputs and a single output. What is the minimum number of LUTs that would be required to implement this circuit? Give an example of a 12 input circuit that could be implemented with this number of LUTs. Give a circuit using LUTs that implements the expression shown below. Uses as few LUTs as you can. How does the number of LUTs compare to the minimum number required for a 12 input function. (A+B+C+D+E)(P+G+H+I+])(K+L) NM wwbcr at: MATE (Q 4(- 2:2! I i f?“ TMPmWS 0» lZ Ware mo, :3 =(¢>< +E)( tea—L3 72L: e/‘rc cu? [144/9 /e. wad; ‘A/LQ, zanméfi Dal We [”503 are “fig“m‘l/CZS 546mm- f?!“ M 4 45/75, Lulu? L} M Wain/am; ...
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