Counting Bits

GowriKumar Chandramouli
GowriKumar Chandramoulisoftware developer at Synopsys India Pvt. Ltd.
••
Counting the number of bits set CH Gowri Kumar [email_address]
Copyright Notice ,[object Object],[object Object],[object Object],[object Object],[object Object]
Problem Statement ,[object Object],[object Object],[object Object],[object Object],[object Object]
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
+ + + + + + + + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
C code ,[object Object]
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
+ + + + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
C code ,[object Object],[object Object]
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
+ + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
C code ,[object Object],[object Object],[object Object]
+ 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
+ 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
C code ,[object Object],[object Object],[object Object],[object Object]
Code for 32-bit integers ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Reference ,[object Object]
The End
1 of 78

Counting Bits

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This ppt describes one of the interesting algorithms to count the number of bits set in an unsigned integer. x = (x & 0x55555555) + ((x>>1)&0x55555555)); x = (x&0x33333333) + ((x>>2)&0x33333333); ... ....

GowriKumar Chandramouli
GowriKumar Chandramoulisoftware developer at Synopsys India Pvt. Ltd.

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Counting Bits

  • 1. Counting the number of bits set CH Gowri Kumar [email_address]
  • 2.
  • 3.
  • 4. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
  • 5. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
  • 6. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
  • 7. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
  • 8. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
  • 9. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1
  • 10. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
  • 11. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
  • 12. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
  • 13. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0
  • 14. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0
  • 15. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0
  • 16. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0
  • 17. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 18. 0 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 19. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1
  • 20. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 21. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 22. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 23. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 24. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 25. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 26. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1
  • 27. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 1 0 0 0 0 1 1 0 0 0 1
  • 28. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 29. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 30. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 31. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1
  • 32. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1
  • 33. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1
  • 34. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1
  • 35. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 1 0 0 0 1 1 1 0 0 0 1
  • 36. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0 0 0 1
  • 37. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
  • 38. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
  • 39. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 1
  • 40. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
  • 41. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
  • 42. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1 0 1
  • 43. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
  • 44. + + + + + + + + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1 0 1 1 0 0 1 0 0 0 0 1 1 0 0 0 1
  • 45. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
  • 46.
  • 47. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
  • 48. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
  • 49. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
  • 50. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1
  • 51. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1
  • 52. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 0 1
  • 53. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
  • 54. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
  • 55. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1
  • 56. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1
  • 57. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1
  • 58. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0 0 0 0 1
  • 59. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
  • 60. + + + + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 1 0 1 0 0 0 0 1 0 0 1 0 1 0 1 0 0 0 0 1 0 0 0 0 1
  • 61. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
  • 62.
  • 63. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
  • 64. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
  • 65. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0
  • 66. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0
  • 67. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 0
  • 68. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
  • 69. + + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 0 1 0 0 1 1 0 0 0 1 0 0 1 0 0 0 0 1 0 0 1 0
  • 70. 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
  • 71.
  • 72. + 0 1 0 0 0 1 1 0 0 0 0 1 0 0 1 1 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
  • 73. + 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 1 1 0 0 0 0
  • 74. 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0
  • 75.
  • 76.
  • 77.