Truth table to equation question (comp Sci)

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SUMMARY

The discussion focuses on converting logical expressions into equivalent forms using NAND gates and inverters. The solutions provided include F1 = xy' + x'y = x ⊕ y (XOR) and F2 = xy (AND). For part b, the challenge is to derive an equation using only NAND gates, which involves implementing xy' and x'y with AND gates, followed by an OR gate. The method described utilizes DeMorgan's law to transform the circuit into NAND configurations by applying inverters at the connections.

PREREQUISITES
  • Understanding of Boolean algebra and logic gates
  • Familiarity with DeMorgan's theorem
  • Knowledge of NAND gate functionality
  • Experience with digital circuit design
NEXT STEPS
  • Study the implementation of NAND gates in digital circuits
  • Learn about DeMorgan's theorem applications in circuit design
  • Explore the principles of XOR and AND gate operations
  • Research techniques for simplifying Boolean expressions
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Students in computer science, electrical engineering students, and anyone interested in digital logic design and circuit simplification techniques.

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Homework Statement


http://imgur.com/BSntip0

The Attempt at a Solution



for part a, i got the solution to be F1 = xy'+x'y= x⊕y (XOR) , F2 = x .y (AND)

for part b i don't understand how i would derive an equal equation that uses only NAND which is (xy') and inverter which is x'
 
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You can start by implememting xy' and x'y with AND gates and their sum with an OR gate. So you have two ANDS feeding an OR. Now on each line connecting an AND with the OR, put two bubbles, one on the AND output and the other on the OR input. The two bubbles are cancelling inverters, but they make the ANDS into NANDS and you have an OR gate with inverted inputs. What does DeMorgan's law tell you that makes?
 

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