Discrete Mathematics

---------------------------SYMBOLIC

LOGIC

77

We will use the same circuit as in Fig. 1.7 except now we label it as in Fig. 1.8.

p q

z

Fig.

1.8:

Determining the

output

of

a combinational circuit

If

we

look at the circuit in Fig. 1.8 and ignore the labels

on

the wires (such as the one that says (p

"q),

we can rederive those labels.

We

start

out

by looking at all the gates where all the inputs are known. Initially, this

is

the top left AND

gate, where we know the inputs

p and q and the two

NOT

gates, one with input p and one with input

q.

We can calculate both the output

of

the AND gate (which is (p

1\

q)) as well as both inverters (one has