Constructing Truth Table based on Circuit Diagram: the case of flip-flops
S-R flip flop using NOR gates:
If S-R flip flop is constructed out of NOR gates, then it detects 1's. Assume the circuit is
constructed as: Q = R NOR Q' and Q'= S NOR Q. If you just trace the signals through the
gates, the truth table can be constructed as:
R
0
0
0
S
0
0
1
Q
0
1
0
Q'
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
Qnext
0
1
0, then 1
(when Q'
switches
from 1 to 0)
1
0
0
1
1
1
1
0
1
1
0
0
0
Q'next
1
0
0
0
1
0, then 1
(when Q
switches
from 1 to 0)
0
0
The last sentence in the last paragraph on p.116 of the textbook, is a cryptic reference to
the behavior of switching the output state as shown in the table above in rows 3 and 6.
The problem with S=1=R is that it produces Q=Q' output state, which is incorrect.
Furthermore, there is a problem with switching over from state S=R=1 to state S=R=0,
because then we have a race (it can be seen from the Karnaugh table, it is a hazard.)
Therefore, we don't use the state S=R=1.
S-R flip flop using NAND gates:
If S-R flip flop is constructed out of NAND gates, then it detects 0's. Note: it must have
the same truth table as the S-R flip flop constructed using NOR gates.
Try 1: Assume the circuit is constructed as: Q = R NAND Q' and Q'= S NAND Q. If you
just trace the signals through the gates, the truth table can be constructed as below - and it
is not the truth table we want:
R
0
0
0
S
0
0
1
Q
0
1
0
Q'
1
0
1
Qnext
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
Q'next
1
1
1, then 0
(when Q
switches
from 0 to 1)
0
1
1
1
0
Try 2:
Therefore, if an S-R flip flop is constructed out of NAND gates, we must feed the gates
with inverted S and R in order to obtain the truth table we want (i.e. Q = R' NAND Q' and
Q' = A NAND Q). So we invert the above truth table (and we should get the first truth
table, if we complement the output):
R
1
1
1
1
0
0
0
0
S
1
1
0
0
1
1
0
0
R'
0
0
0
0
1
1
1
1
S'
0
0
1
1
0
0
1
1
Q
0
1
0
1
0
1
0
1
Q'
1
0
1
0
1
0
1
0
Qnext
1
1
1
1
0
0
0
1
Q'next
1
1
0
0
1
1
1
0
JK Flip flop:
Assume that S = J AND Q', and R = K AND Q (there was a typo in the notes, we used
NAND instead of AND). Given J and K, R and S are calculated according to those
formulas. Then Qnext and Q'next are calculated based on the R-S flip flop truth table.
J
0
0
0
0
1
1
1
1
K
0
0
1
1
0
0
1
1
Q
0
1
0
1
0
1
0
1
Q'
1
0
1
0
1
0
1
0
R = K AND Q
0
0
0
1
0
0
0
1
S = J AND Q'
0
0
0
0
1
0
1
0
Reference:
http://www.shef.ac.uk/physics/teaching/phy107/.
Qnext
0
1
0
0
1
1
1
0
Q'next
1
0
1
1
0
0
0
1