FUSE NUMBERS

FUSE NUMBERS

Consider X, Y and Z is three variable, To Fuse the three variable into single variable and result does not match to other X, Y and Z combination

Solutions:

X=0:100

Y=0:100

Z=0:100

Normal Fuse method

O=X+Y+Z

This method

Consider X=1, Y=3, Z=3

O=1+3+3= 7

But this result match to

X=1, Y=2, Z=4,

O=1+2+4= 7

(1+3+3)==(1+2+4)

So this not unique for all combination

Another method is binary to decimal converter method

Ex:

0 0 0 = 0

0 0 1 = 1

0 1 0 = 2

0 1 1 = 3

1 1 0 = 4

1 0 1 = 5

1 1 0 = 6

1 1 1 = 7

How is it working?

Three combination X, Y, Z

Max binary counts =2 (0 or 1)

So,

O = 2^2*X + 2^1*Y + 2^0*Z

Finally integer fusion

O = M^2*X+M^1*Y+M^0*Z

Where M is a max number of (X, Y and Z) +1

Here M= 100+1

So, Output is

O = 101^2*X+101^1*Y+101^0*Z

Implemented by MATLAB Program

clc

clear all

close all

X=0:100;        % X is 0 to 100

Y=0:100;        % Y is 0 to 100

Z=0:100;        % Z is 0 to 100

figure(1)

subplot(2,2,1),plot(X,'g-'),title('X value');   % plot  X is linear

subplot(2,2,2),plot(Y,'b-'),title('Y value');   % plot Y is linear

subplot(2,2,3),plot(Z,'y-'),title('Z value');   % plot Z is linear

M=101;

k1=0;

O=zeros(length(X)*length(Y)*length(Z),1);

for i=1:length(X)

    for j=1:length(Y)

        for k=1:length(Z)

            k1=k1+1;

            O(k1)=M^2*X(i)+M^1*Y(j)+M^0*Z(k);       % Add different combination of X, Y and Z,

        end

    end

end

subplot(2,2,4),plot(O,'r-'),title('Output value');  % Output also linear

Result