Converting to just NANDs with DeMorgan's

[Melawrghk]

Homework Statement

Convert a₃'a₁ + a₃'a₂ + a₃'a₀ + a₃a₂'a₁'a₀'

to an expression (well, it's a circuit eventually) that would only employ NAND and NOR gates. Use DeMorgan's Law.

Homework Equations

a'+b'=(ab)'

The Attempt at a Solution

I applied DeMorgan's as the problem suggested...

(a₃'a₁)''+(a₃'a₂)''+(a₃'a₀)'' + (a₃a₂'a₁'a₀')''

Which yielded:
( (a₃'a₁)' (a₃'a₂)' (a₃'a₀)' (a₃a₂'a₁'a₀')')'

This is in just NAND and NOR gates, but the circuit isn't really aesthetically appealing... Is there a simplifying trick I'm missing? Or is this just what it is supposed to be?

Thanks in advance!

 

[mplayer]

I would draw out the circuit first before doing any Boolean algebra using regular AND OR and INVERTER gates. Then when its all drawn, convert the AND and NOR gates to NAND and NOR. Put inverter circles on the inputs of the and OR gates to turn them into NANDs, and inverter circles on the output of the AND gates to turn them into NAND gates. Cancel out and redundant inverters. Should results in a full NAND-NAND realization of you circuit.

 

[Mene]

Great job on applying DeMorgan's Law to convert the expression to just NAND and NOR gates! The circuit may not look aesthetically appealing, but it is a correct and simplified representation of the original expression. Sometimes, in order to achieve a specific logic function, the circuit may not look pretty but it is still functional. Keep up the good work!