Design 101 sequence detector (Mealy machine)

Prerequisite – Mealy and Moore machines
A sequence detector is a sequential state machine that takes an input string of bits and generates an output 1 whenever the target sequence has been detected. In a Mealy machine, output depends on the present state and the external input (x). Hence, in the diagram, the output is written outside the states, along with inputs. Sequence detector is of two types: 

1. Overlapping
2. Non-Overlapping

In an overlapping sequence detector, the last bit of one sequence becomes the first bit of the next sequence. However, in a non-overlapping sequence detector, the last bit of one sequence does not become the first bit of the next sequence. In this post, we’ll discuss the design procedure for non-overlapping 101 Mealy sequence detectors. 

Examples: 

For non overlapping case
Input :0110101011001
Output:0000100010000

For overlapping case
Input :0110101011001
Output:0000101010000

The steps to design a non-overlapping 101 Mealy sequence detectors are: 

Step 1: Develop the state diagram –
The state diagram of a Mealy machine for a 101 sequence detector is: 

Step 2: Code Assignment –

Rule 1 : States having the same next states for a given input condition should have adjacent assignments. 
Rule 2: States that are the next states to a single state must be given adjacent assignments. 
Rule 1 given preference over Rule 2. 

The state diagram after the code assignment is: 

Step 3: Make Present State/Next State table –
We’ll use D-Flip Flops for design purposes. 

Step 4: Draw K-maps for Dx, Dy and output (Z) –

Step 5: Finally implement the circuit –

This is the final circuit for a Mealy 101 non-overlapping sequence detector.