Self-Correcting Circuits

Self-Correcting Circuits

All states = Valid states + invalid states. Invalid states: unused or error states.

Danger: circuit may start or arrive at an invalid state and stay at invalid states circuit malfunction!

To avoid this, we can analyze if our circuit is self-correcting, and re-design the circuit to be self-correcting if it is not so.

A circuit is self-correcting if there are no cycles among its invalid states. It may start in an invalid state but will eventually end up in a valid state for proper functioning.

Self-Correcting Circuits

Analysis to check for self-correcting circuit: Obtain complete state diagram of circuit Identify invalid states Check if there is a cycle among the invalid states

The absence of a cycle among invalid states implies a self-correcting circuit.

Self-Correcting Circuits

Take design example #3. We obtained the following expressions:

SA = B.x SB = A'.B'.x SC = x'RA = C.x' RB = B.C + B.x' RC = x

y = A.x

We fill the X’s in the state table with their values, including all unused states 000, 110 and 111.

Self-Correcting Circuits State table according to derived expressions.

Present Nextstate Input state Flip-flop inputs Output

A B C x A+ B+ C+ SA RA SB RB SC RC y

0 0 0 0 0 0 0 0 1 0 0

0 0 0 1 0 0 1 0 0 1 0

0 0 1 0 0 0 1 0 1 0 0 1 0 0

0 0 1 1 0 1 0 0 0 1 0 0 1 00 1 0 0 0 1 1 0 0 0 0 1 0 00 1 0 1 1 0 0 1 0 0 1 0 1 00 1 1 0 0 0 1 0 1 0 1 1 0 00 1 1 1 1 0 0 1 0 0 1 0 1 01 0 0 0 1 0 1 0 0 0 0 1 0 01 0 0 1 1 0 0 0 0 0 0 0 1 11 0 1 0 0 0 1 0 1 0 0 1 0 01 0 1 1 1 0 0 0 0 0 0 0 1 11 1 0 0 0 0 0 0 1 0 01 1 0 1 1 0 0 1 0 1 11 1 1 0 0 1 0 1 1 0 01 1 1 1 1 0 0 1 0 1 1

Unu

sed

stat

es

1 1 11 0 00 0 11 0 0

0 0 10 1 0

Self-Correcting Circuits

State diagram according to state table.

001

1/0

0/0

1/00/0

0/0

0/0

0/0

1/0 1/1

1/1

1/1

0/0

1/1

011

100

1/0

101 010

000

110

111

0/0

0/0

No cycle among invalid states, hence circuit is self-correcting.