Sequential Circuits

SEQUENTIAL CIRCUITS

Sequential circuits are combinational circuits with a feedback element in their circuitry path that includes one or more memory elements.

Latch A latch is a 1-bit memory element. You can capture a single bit in a latch at one instant and then use it later.

for example, when adding numbers you can capture the carry-out in a latch and use it as a carry-in in the next calculation.

Register The register is just m latches in a row and is able to store an m-bit word that is, the register is a device that stores one memory word. A computer’s memory is just a very large array of registers.

Shift register A shift register is a special-purpose register that can move the bits of the word it holds left or right; for example the 8-bit word 00101001 can be shifted left to give 01010010.

Counter A counter is another special-purpose register that holds an m-bit word. However, when a counter is triggered (i.e. clocked) its contents increase by 1

for example, if a counter holding the binary equivalent of 42 is clocked, it will hold the value 43. Counters can count up or down, by 1 or any other number, or they can count through any arbitrary sequence.

State machines A state machine is a digital system that moves from one state to another each time it is triggered. Ultimately, the computer itself is a nothing more than a state machine controlled by a program and its data.

SR LATCH

The SR latch, made of two 2-input NOR gates, which is the simplest interesting sequential circuit.

SYNCHRONOUS SEQUENTIAL LOGIC

The circuits considered so far are examples of asynchronous sequential logic circuits.

ASYNCHRONOUS SEQUENTIAL LOGIC

In an asynchronous circuit, the state of the circuit, ie the value on the fed back signal(s), can change at any time in response to an input change. Asynchronous circuits are tricky to design,

• The general way of representing the sequential circuit is shown in the following figure :

• To check a sequence of symbols, the circuit is started in the state corresponding to the DFA start state, and the input symbol sequence is presented on the inputs to the circuit, one symbol per clock cycle. The circuit moves between states, one state transition per clock cycle, and the output indicates at any time whether or not it is in an accepting state.