---
author: Oldrich Pecak
---

# Sequential circuits

---

## Automata basics

- sequential circuits are finite state automata
- requires some memory to remember state
- can be formalized:
    - set of states
    - initial state
    - transition function
    - output function
- two types:
    - Mealy
    - Moore
- we will focus on synchronized automata

---

## Mealy and Moore automata

- Mealy:
    - output derived from current state and input
    - output can change without change in state
    - can result in simpler automata
- Moore:
    - output derived from current state

---

## Encoding states

- we work with 1 bit memory cells (flip flops)
- minimalize number of cells:
    - encoding values
    - more complex transition function
    - possibly slower
- simple solution:
    - 1 in N encoding
    - possibly faster
    - simple to work with

---

## Transition function

- describes the behaviour of the automata
- multiple representations
    - transition matrix
    - set of pairs
    - text description
    - state graph
    - time diagram

---

## Output function

- combinational circuit
- can be very simple (depends on encoding and type)
- usually multiple outputs

---

## Constructing automata

- flip-flop/latch selection matters
- transition function must be transfered into driving functions
- my tip:
    - use 1 in N encoding
    - use D flip-flops
- do not forget reset/initialization inputs

---

## Some notes on automata

- very similar to regular finite automata
- some algorithms for minimalization work on both
- not fully interchangeable!

---

## Let's build something II

- pulse length counter
- if input pulse is shorter than 2 cycles, output a single cycle 1 after it ends

---

## Let's build something

- time-exclusive XOR
- works like XOR, but also looks 1 cycle into the past