I am trying to solve these problems with truth tables using the formulas below. I am having a problem with the NOT to NAND
I think i got the first 2 problems correct using: AND is equivalent to NOR, AND is equivalent to NAND
The equations for AND, OR and NOT using the NAND operator are:
X + Y = x' NAND y' ??
X * Y =
X' = X NAND 1
The equations for AND, OR and NOT using only the NOR operator are:
X' = ?
X + Y = (X NOR Y) NOR 0
X * Y = X' NOR Y' ??
I am trying to follow this formula
An OR gate with a NOT in both inputs is equivalent to a NAND.
An AND gate with a NOT in both inputs is equivalent to a NOR.
An OR gate with a NOT in its output is equivalent to a NOR.
An AND gate with a NOT in its output is equivalent to a NAND.
this is how i worked out AND to NOR equivalent
X Y X AND Y X NOR Y
-----------------------------
0 0 0 1
0 1 0 0
1 0 0 0
1 1 1 0
X' Y' X' NOR Y'
-------------------
1 1 0
1 0 0
0 1 0
0 0 1
My biggest problem is how do i use a NOT in the outputs in a truth table? Also, how would i go from a NOT to a NOR? I want to work all these out in a truth table.
X * Y = "An AND gate with a NOT in its output is equivalent to a NAND."
what are the outputs in a truth table? and how can i go from a X' to equivalent NAND?
We know that,
X X'
------
0 1
1 0
Hence,
X X NOR X
------------
0 1
1 0
So we get,
X' = X NOR X
For your second question, suppose you have two inputs X' & Y' and you want to get to X NAND Y,
X NAND Y = (X AND Y)' = X' OR Y' (by DeMorgan's Law)
Hence, the truth tables are as follows:
X Y X AND Y (X AND Y)'
-----------------------------
0 0 0 1
0 1 0 1
1 0 0 1
1 1 1 0
X Y X' Y' X' OR Y'
-----------------------------
0 0 1 1 1
0 1 1 0 1
1 0 0 1 1
1 1 0 0 0