Implementing a Logic Circuit with NAND & NOR Gates

[Sinister]

Homework Statement

Given the above circuit, implement the logic circuit with only NAND gates, and then one with only NOR gates.

Homework Equations

N/A

The Attempt at a Solution

I made a truth table but I'm pretty sure its wrong because I'm confused on how to implement the 'g' part of the circuit.

Is there an easier way of doing this?

 

[gneill]

Do you know how to form NOT gates from either a NAND gate or a NOT gate?
Do you know how to transform a NAND into a NOR and vice-versa?
Individual ANDs and ORs can obviously be transformed to NANDs and NORs if you tack a NOT gate on after them...

You can go through the circuit and make the conversions, then cancel all the redundant NOTs that appear.

 

[Sinister]

Do you know how to form NOT gates from either a NAND gate or a NOT gate?
Do you know how to transform a NAND into a NOR and vice-versa?
Individual ANDs and ORs can obviously be transformed to NANDs and NORs if you tack a NOT gate on after them...

You can go through the circuit and make the conversions, then cancel all the redundant NOTs that appear.

Is there no way to solve it mathematically?
I really don't like memorizing these types of concepts

 

[gneill]

Is there no way to solve it mathematically?
I really don't like memorizing these types of concepts

I suppose there must be, but it seems a lot of work to translate from a pictorial circuit to a mathematical form, then do the work, then convert back to a pictorial form. You can "do the math" visually right on the diagram by knowing a rather small number of "translations". Really, the method is practically algebraic in its methodology.

 

[Sinister]

Ok so I understand that not gate and the and gate form a NAND gate, and then the two NAND gates form another NAND gate. But then I get confused, and especially with part on the right hand side.
Care to explain the transformation?

 

[gneill]

Ok so I understand that not gate and the and gate form a NAND gate, and then the two NAND gates form another NAND gate. But then I get confused, and especially with part on the right hand side.
Care to explain the transformation?

In the following figure are the basic transformations. Read the lines of figures across the page; all the gate configurations on the same line are equivalent.

The yellow circles represent NOT operations that need to be added for the given gate type to stay equivalent to the others in the line. The important things to remember are:

1. How to make a NOT gate out of either a NAND or a NOR
2. If you move the NOT from output of a NAND or NOR to its input leads, the basic gate changes type (from AND to OR or from OR to AND). Thus if you remove the NOT circle from the tip of an NAND gate and place two such circles on the input leads, then change the gate type to an OR to preserve the the overall function.
3. You can migrate the NOT circles along the continuous path of a circuit wire. Thus you can change their association from one gate to another. This can be used to transform gate types (for example, taking the NOT circle from a NAND turns it into a AND, and the moved circle might cancel with one along, or at the other end of, the same wire). NOTs in series cancel in pairs.

 

[Sinister]

Wow,
THANK YOU SO MUCH!