Convert octal to decimal number

Illustrated examples for converting octal numbers to equivalent decimal number.

Problem 1: Convert ( 237 )₈= ( ? )<sub>10


=  2 3 7</sub>
   ↑      ↑
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

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Problem 2: Convert ( 1000 )₈= ( ? )<sub>10


=  1 0 0 0</sub>
    ↑        ↑
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

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Problem 3: Convert ( 7777 )₈= ( ? )<sub>10


=  7 7 7 7</sub> 
    ↑        ↑
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

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Problem 4: Convert ( 2 0 )₂= ( ? )<sub>10


=  2 0</sub>
   

= 2 x 8¹+ 0 x 8⁰


= 2 x 8  + 0 x 1


= 16  +  0 


= 16


Therefore  ( 2 0 )₈ =  ( 1 6 )₁₀