prelab9_soln

# prelab9_soln - Physics 3330 Prelab 9 solutions 1 NOR gate A...

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Unformatted text preview: Physics 3330 Prelab 9 solutions 1. NOR gate A B A + B 1 1 1 1 1 NAND gate A B A Â· B 1 1 1 1 1 1 1 NOT gate A A 1 1 XOR gate A B A âŠ• B 1 1 1 1 1 1 2. Left side A B A + B A + B 1 1 1 1 1 1 1 1 right side A B A B A Â· B 1 1 1 1 1 1 1 1 1 The truth tables are the same for both sides of DeMorganâ€™s second theorem so A + B = A Â· B . Below are the derivations using the laws of Boolean algebra. A + A Â· B = A Â· 1 + A Â· B = A (1 + B ) = A Â· 1 = A A Â· ( A + B ) = A Â· A + A Â· B = A + A Â· B = A (1 + B ) = A A + A Â· B = ( A + A Â· B ) + A Â· B = A + ( A + A ) B = A + B 1 3. The XOR function is often written as A âŠ• B = AB + A B but it can also be written the way most people think of it (either A or B and not both A and B) which gives A âŠ• B = ( A + B ) Â· ( A Â· B ). These two formulations can be shown to be equivlanet: ( A + B ) Â· ( A Â· B ) = ( A + B ) Â· ( A + B ) = ( A + B ) A +( A + B ) B = A A + B A + A B + B B = B A + A B Starting from the second formulation we can get to a relatively simple circuit composed of just NAND and NOR gates....
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prelab9_soln - Physics 3330 Prelab 9 solutions 1 NOR gate A...

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