Construction of the machines to produce residue modulo β2β of binary numbers
Prerequisite: Mealy and Moore Machines, Difference between Mealy machine and Moore machine
In this article, we will see some designing of Finite Automata with Output i.e, Moore and Mealy machines.
Problem: Construction of the machines that take the binary number {0, 1} as input and produce residue modulo β2β as output i.e, when the equivalent decimal number of binary input over {0, 1} is divided by 2 then it gives output as itβs remainder.
Assume,
Ξ = {0, 1} and Ξ = {0, 1}
where Ξ and Ξ are the input and output alphabet respectively.
The required Moore machine is constructed below:
In the above diagram, the initial state βXβ on getting β0β as the input it remains in the state of itself and prints β0β as the output and on getting β1β as the input it transmits to a state βYβ and prints β1β as the output so on for the remaining states.
For example, when the input string is β10β then above Moore machine produce 0 as the output because the decimal equivalent of binary input β10β is 2 and 2 divided by 2 is 0 i.e, the remainder is 0. Thus finally above Moore machine can easily produce residue modulo β2β as output i.e, when the equivalent decimal number of binary input over {0, 1} is divided by 2 then it gives output as itβs remainder.
The required Mealy machine is constructed below:
In the above diagram, the initial state βXβ on getting β0β as the input it remains in the state of itself and prints β0β as the output and on getting β1β as the input it transmits to a state βYβ and prints β1β as the output. The state βYβ on getting β1β as the input it remains in the state of itself and prints β1β as the output and on getting β0β as the input it goes back to the initial state βXβ and prints β0β as the output.
For example, when the input string is β10β then above Mealy machine produce 0 as the output because the decimal equivalent of binary input β10β is 2 and 2 divided by 2 is 0 i.e, the remainder is 0. Thus finally above Mealy machine can easily produce residue modulo β2β as output i.e, when the equivalent decimal number of binary input over {0, 1} is divided by 2 then it gives output as itβs remainder.