Range:   w (0, 0.15)         x (0.15, 0.25)

              y (0.25, 0.95)       z (0.95, 1)

Formulae: $l_n = l_{n-1} + ( U_{n-1} – l_{n-1} ) F_n-1 (x)$

                  $U_n= l_{n-1} + ( U_{n-1} – l_{n-1} ) F_n (x)$

a) Initially $U_0 = 1 \ and \ l_0 =0$

  i. For x:

    $l_n$ = 0+ (1-0) × 0.15 =0.15

    $U_n$ = 0 + (1-0) × 0.25 = 0.25

    Tag for x = ( 0.15, 0.25)

  ii. Tag for y:

    $l_n$ = 0.15 + (0.25 – 0.15 ) × 0.25 = 0.175

    $U_n$ = 0.245

    Tag for xy = (0.175, 0.245)

  iii. Tag for z

    $l_n$ = 0.175 + (0.245 – 0.175) × 0.75 = 0.2415

    $U_n$ = 0.175 + (0.245 – 0.175) × 1 = 0.245

    Tag for xyz = (0.245 , 0.245)

  iv. Tag for w

    $l_n$ = 0.2415 + (0.245 – 0.2415) × 0 = 0.2415

    $U_n$ = 0.2415 + (0.245 – 0.2415) × 0.15 = 0.242025

    Tag for xyzw = (0.242025 , 0.2415)

  v. Tag for z

    $l_n$ = 0.2415 + ( 0.242025 – 0.2415) × 0.9 = 0.24199875

    $U_n$ = 0.2415 + (0.242025 – 0.2415 ) × 1 = 0.242025

    Tag for xyzwz = (0.24199875, 0.242025)

  Tag generated for the sequence =

  Tag generated for the sequence xyzwz = = 0.242011875

b) Deciphering the tag

  Tag obtained = 0.242011845

  Range of Symbols :

    w (0, 0.15)         x (0.15, 0.25)

    y (0.25, 0.95)         z ( 0.95, 1)

    New tag (T ’ ) =

i. Tag obtained lies in range of x

  First decoded symbol = ‘x’

  T = = 0.9201

 ii. Tag obtained lies in range of y

    Next Symbol = ‘y’

    T = = 0.9573

 iii. Tag obtained lies in range of z

    Next Symbol = ‘z’

    T = = 0.1463

 iv. Tag generated lies in range of w

    Next Symbol = ‘w’

    T ‘ = = 0.975

 v. Tag generated lies in the range of z

    Next Symbol ‘Z’

    T ‘ = = 0.5

    Generating sequence till symbols we get the sequence xyzwz