How to Construct Basic Logic Gates from Nand Gate Using Bool Algebra

Nand Gate

(ab)’

Not Gate

a’ = (aa)’  

Or Gate

Step 1: (a + b) = ((a + b)’)’ = (a’b’)’ = ((aa)’(bb)’)’

Step 2: A = (aa)’,B =(bb)’

Step 3: (a+b) = (AB)’

And Gate

Step 1: ab = ((ab)’)’

Step 2: A = (ab)’

Step 3: ab = (A)’ = (AA)’

Bool Algebra Laws

Idempotency theorem:

x+x=x

xx=x

 

DeMorgan’s theorem:

(xy)’=x’+y’     

(x+y)’ = x’y’