Convert octal to decimal number

Illustrated examples for converting octal numbers to equivalent decimal number.

Problem 1: Convert ( 237 )8= ( ? )10


=  2 3 7
   ↑      ↑
MSB    LSB

= 2 x 82 + 3 x 81 + 7 x 80


= 2 x 64 + 3 x 8 +  7 x 1


= 128 + 24  + 7


= 159


Therefore  ( 2 3 7 )8 =  ( 1 5 9 )10



Problem 2: Convert ( 1000 )8= ( ? )10


=  1 0 0 0
    ↑        ↑
MSB       LSB

= 1 x 83 + 0 x 82 + 0 x 81+ 0 x 80


= 1 x 512  + 0 x 64   + 0 x 8  + 0 x 1


= 512  +  0  +  0  +  0


= 512


Therefore  ( 1 0 0 0 )8 =  ( 5 1 2 )10




Problem 3:
 Convert ( 7777 )8= ( ? )10


=  7 7 7 7 
    ↑        ↑
MSB      LSB

= 7 x 83 + 7 x 82 + 7 x 81+ 7 x 80


= 7 x 512  + 7 x 64   + 7 x 8  + 7 x 1


=  3584 +  448  +  56  +  7


= 4095


Therefore  ( 7 7 7 7 )8 =  ( 4 0 9 5 )10





Problem 4: Convert ( 2 0 )2= ( ? )10


=  2 0
   
= 2 x 81+ 0 x 80


= 2 x 8  + 0 x 1


= 16  +  0 


= 16


Therefore  ( 2 0 )8 =  ( 1 6 )10

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