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I have a circuit that has 4 inputs and am only allowed to use 5-, 3- and 2-input NAND gates. Yes this is an assignment question but I have already solved the design of the circuit.

I just don't know how to use (if possible) 4 outputs with a 5-input NAND gate.

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You can use 5 input nand and only use 4 of the inputs. Make sure you tie the unused input high (logic 1).

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    \$\begingroup\$ Another solution is to fan out one of the inputs into two inputs of the NAND gate (similarly to how a NOT is made from a binary NAND). not(P and P and Q) is not(P and Q). You solution relies on P and T = P, and this one on P and P = P. \$\endgroup\$ – Kaz Apr 6 '13 at 3:39
  • \$\begingroup\$ For the NAND gate to produce a logic low ALL inputs must be at logic high. You may accomplish this by whatsoever means your heart may desire. The least resource constraining is to connect the extra input to a logic high source permanently. Another method (as Kaz says) is to connect one of the sources to two on the NAND inputs. This loads the source with two input loads. In many applications and logic families this is trivially unimportant. In a few case the extra loads affect on timing or additional power needs may be important. In a very few logic families "fanout" may make this important. \$\endgroup\$ – Russell McMahon Jul 21 at 13:14
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For the NAND gate to produce a logic low ALL inputs must be at logic high.
You may accomplish this by whatsoever means your heart may desire.

The least resource constraining method is to connect the extra input to a logic high source permanently.

Another method (as Kaz says) is to connect one of the sources to two of the NAND inputs.
This loads the source with two input loads.
In many applications and logic families this is trivially unimportant.

  • In a few case the extra loads affect on timing or additional power needs may be important.

  • In a very few logic families "fanout" (the number of inputs that can be driven by a source) may make this important. This MAY happen in rare cases if a gate from a given family is driving a gate of the same family, but is more likely to occur if families are mixed or if a source that is not a gate is being used.

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