Page 61 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

42 ChaptevFive

Actually, if you want to go down this path, you can construct all of the
above functions using one or more NAND gates (or one or more NOR gates).
For example, if you connect the two inputs of a NAND gate together, you end
up with a NOT as shown in Figure 5-8 (you can achieve the same effect by

connecting the two inputs of a NOR gate together).

-PFp y

TT F

NAND acting a5 NOT

Figure 5-8. Forming a NOT from a NAND

As the inputs a and b are connected together, they have to carry identical
values, so we end up showing only two rows in the truth table. We also know
that if we invert the output from a NAND, we end up with an AND. So we
could append a NAND configured as a NOT to the output of another NAND
to generate an AND (Figure 5-9).

a
-
w Y T
b
-

NAND NAND acting a5 NOT TF T F
T TIFIT
Figure 5-9. Forming an AND from two NANDs

Later on in Chapter 9, we’ll discover how to transform functions formed
from ANDs into equivalent functions formed from ORs and vice versa.
Coupled with what we’ve just seen here, this would allow us to build anything
we wanted out of a bunch of 2-input NAND (or NOR) functions.