Sequential circuit: What does state mean exactly?

I have read some posts like: What is state in a sequential circuit? about explaining what a state is in the sequential logic circuit. But the responses are pretty much the same as those ones in my textbook and I still don't understand what it is exactly.

From my understanding so far, I think a state is pretty much like the mode of a circuit when some certain inputs are given. For example, if we have a two-inputs SR latch, when S and R are 1 and 0, SR latch is in the set state, which I think it's like the circuit is in the setting/saving mode. (not sure if this understanding is correct or not)

But if this understanding is correct, I found out it is so weird to read my textbook. (Digital Design and Computer Architecture, second edition, David Money Harris)

"The chapter begins by studying latches and flip-flops, which are simple sequential circuits that store one bit of state." If state is similar to the concept of mode, why we can tell how many bits are there in a state?

Can someone please give me an accurate definition about the state? If it is possible to provide an analogy I will be really grateful, this would really help me understand this stuff.

• I would think of it like, "What is the state of the light switch in your room right now?" On or off? Set or reset? 1 or 0? Commented Apr 17, 2019 at 22:45
• One additional question that is not included in the description above. Given N inputs, how do I know how many possible states are there in a sequential circuit? Commented Apr 17, 2019 at 22:46
• N inputs can have 2^N states, but some may be X don't care "State" of the system expresses the unique logical values of all nodes or any 1 node when looking at 1 port Commented Apr 17, 2019 at 22:50
• So can I understand this way? Each row in a truth table is a possible state of the sequential circuit? (without considering if this state is a don't care) Commented Apr 17, 2019 at 22:52
• that's another way to express a state which is static condition Commented Apr 17, 2019 at 22:53

The number of states in a sequential system is not determined by the number of inputs, and it is not determined by the rows of a combinational truth table. Just talking about the "state" of the inputs is misleading (although I do it sometimes).

The number of possible states is determined only by the number of memory bits in the system. The maximum number of states is equal to $$\2^N\$$ if there are $$\N\$$ bits of memory.

The state of system can change how it responds to its inputs. The behavior (outputs) of the system can be different for each of the possible states even when the inputs are the same.

So, if you have 2 memory bits (2 flip-flops) then you have 4 possible states corresponding to the four combinations of '1' and '0' in those two flip-flops. The outputs can have up to 4 different values for exactly the same input based on the current state.

You might have just one input (plus a clock) for your 4-state machine, or you could have a hundred inputs. You might have just one output or many outputs. Nevertheless, if you have two flip-flops you have four possible states.

• how mant states does a CD4017 have is it 10 or 32 (or some other number) Commented Apr 18, 2019 at 1:41
• @Jasen A CD4017 has 5 flip-flops. These flip-flops have the potential of representing 32 different states. However, the combinational logic in the CD4017 makes most of those states unreachable in normal operation...there are only 10 states that can occur under normal circumstances. Commented Apr 18, 2019 at 1:47
• many of the 4017 undesirable states are physically reachable but only by breaking design rules (modulating the power supply, or sending runt pulses into the reset pin) after a few clocks or so the chip returns to its normal cycle of 10 states. Commented Apr 18, 2019 at 3:07