Mealy and Moore Type FSM for Serial Adder

Types of Finite State Machine 

In this article I will discuss Mealy and Moore Type FSM for Serial Adder. But let us just see first that there are two main types of finite state machines (FSM)

Mealy type

Moore type

Mealy type FSM for serial adder:

As we know that mealy model output is based on both present state and the input of the sequential circuits. Let A and B be two unsigned numbers that have to be added to produce sum S. We perform a task of serial addition y adding two inputs A and B for serial adder. For addition we perform a cycle for bit configuration by one by one. It includes three shift registers that are used to hold A, B and S. Then in each clock cycle, a pair of bits is added by the adder FSM, and the end of the cycle the resulting sum bit is shifted into the S register. We use positive-edge-triggered flip-flops in which changes take place soon after the positive edge of the clock, depending on the propagation delays within the various flip-flops. At this time of propagation the contents of all three shift registers are shifted to the right; this shifts the existing sum bit into sum S bit, and it presents the next pair of input bits a and b to the adder FSM.

mealy model
mealy model

For the FSM model the table depends on the given equation,

Y=ab+ ay+ by

For S the equation will be the XOR of inputs and output.

The next state is depending on the two present states G and H having value 0 and 1. In state G the input valuation 00 will produce s = 0 and the FSM will remain in the same state. For input valuations 01 and 10 the output will be s = 1 and the FSM will remain in G. But for 11, s= 0 is generated, and the machine moves to state H. In state H valuations 01 and 10 cause s = 0, while 11 cause s = 1. In all three of these cases, the machine remains in H. However, when the valuation 00 occurs, the output of 1 is produced and a change into state G takes place.

FSM model
FSM model

Moore type FSM for serial adder: 

As we know that Moore’s model output is based on its present state. In mealy model we used only 2 present states but in Moore’s model we required more than 2 states G, G0 and H or H0.

Y1 is simply the XOR of a, b and y2



Moore type FSM for serial adder


Moore’s model for adder


The difference between the Mealy and Moore’s model is that the Moore’s model output s passed through an extra flip flop and there is a delay in clock cycle.

For more detail check

what is the difference between Mealy and Moore models?

Also check

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