I generated the normalized data by writing a simple python script:

import math

img = [
    [52, 55, 61,  66,  70,  61, 64, 73],
    [63, 59, 55,  90, 109,  85, 69, 72],
    [62, 59, 68, 113, 144, 104, 66, 73],
    [63, 58, 71, 122, 154, 106, 70, 69],
    [67, 61, 68, 104, 126,  88, 68, 70],
    [79, 65, 60,  70,  77,  68, 58, 75],
    [85, 71, 64,  59,  55,  61, 65, 83],
    [87, 79, 69,  68,  65,  76, 78, 94]
]

# Number of pixels
N = len(img) * len(img[0])

# Initialize histogram and cumulative distribution function (cdf)
hist = {}
cdf = {}
norm_cdf = {}
for i in range(255):
    hist[i] = 0
    cdf[i] = 0
    norm_cdf[i] = 0

# Create histogram
for row in img:
    for val in row:
        hist[val] += 1

# Create cdf
for i in range(255):
    for j in range(i+1):
        cdf[i] += hist[j]
    norm_cdf[i] = int(math.floor(float(cdf[i]-1)/63*255))

newimg = [
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0],
    [0, 0, 0, 0, 0, 0, 0, 0]
]

for i in range(8):
    for j in range(8):
        newimg[i][j] = norm_cdf[ img[i][j] ]

print '+-------+-----------+-----+----------------+'
print '| %5s | %9s | %3s | %14s |' % ('Value', 'Histogram', 'cdf', 'Normalized cdf')
print '+-------+-----------+-----+----------------+'
for i in range(255):
    if hist[i] == 0: continue
    print '| %5s | %9s | %3s | %14s |' % (i, hist[i], cdf[i], norm_cdf[i])
print '+-------+-----------+-----+----------------+'

print ''
print 'Original subimage:'
print ''
for i in range(8):
    print ('%4d'*8) % tuple(img[i])

print ''
print ''
print 'Equalized subimage:'
print ''

for i in range(8):
    print ('%4d'*8) % tuple(newimg[i])

Sample output:

+-------+-----------+-----+----------------+
| Value | Histogram | cdf | Normalized cdf |
+-------+-----------+-----+----------------+
|    52 |         1 |   1 |              0 |
|    55 |         3 |   4 |             12 |
|    58 |         2 |   6 |             20 |
|    59 |         3 |   9 |             32 |
|    60 |         1 |  10 |             36 |
|    61 |         4 |  14 |             52 |
|    62 |         1 |  15 |             56 |
|    63 |         2 |  17 |             64 |
|    64 |         2 |  19 |             72 |
|    65 |         3 |  22 |             85 |
|    66 |         2 |  24 |             93 |
|    67 |         1 |  25 |             97 |
|    68 |         5 |  30 |            117 |
|    69 |         3 |  33 |            129 |
|    70 |         4 |  37 |            145 |
|    71 |         2 |  39 |            153 |
|    72 |         1 |  40 |            157 |
|    73 |         2 |  42 |            165 |
|    75 |         1 |  43 |            170 |
|    76 |         1 |  44 |            174 |
|    77 |         1 |  45 |            178 |
|    78 |         1 |  46 |            182 |
|    79 |         2 |  48 |            190 |
|    83 |         1 |  49 |            194 |
|    85 |         2 |  51 |            202 |
|    87 |         1 |  52 |            206 |
|    88 |         1 |  53 |            210 |
|    90 |         1 |  54 |            214 |
|    94 |         1 |  55 |            218 |
|   104 |         2 |  57 |            226 |
|   106 |         1 |  58 |            230 |
|   109 |         1 |  59 |            234 |
|   113 |         1 |  60 |            238 |
|   122 |         1 |  61 |            242 |
|   126 |         1 |  62 |            246 |
|   144 |         1 |  63 |            250 |
|   154 |         1 |  64 |            255 |
+-------+-----------+-----+----------------+

Original subimage:

  52  55  61  66  70  61  64  73
  63  59  55  90 109  85  69  72
  62  59  68 113 144 104  66  73
  63  58  71 122 154 106  70  69
  67  61  68 104 126  88  68  70
  79  65  60  70  77  68  58  75
  85  71  64  59  55  61  65  83
  87  79  69  68  65  76  78  94

Equalized subimage:

   0  12  52  93 145  52  72 165
  64  32  12 214 234 202 129 157
  56  32 117 238 250 226  93 165
  64  20 153 242 255 230 145 129
  97  52 117 226 246 210 117 145
 190  85  36 145 178 117  20 170
 202 153  72  32  12  52  85 194
 206 190 129 117  85 174 182 218

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