Convert binary to decimal number

Solved examples of binary to decimal number conversion












Problem 1: Convert ( 10110 )₂= ( ? )<sub>10


=  1 0 1 1 0</sub>
    ↑          ↑
MSB      LSB

= 1 x 2⁴ + 0 x 2³ + 1 x 2² + 1 x 2¹ + 0 x 2⁰


= 1 x 16 + 0 x 8 + 1 x 4 + 1 x 2 + 0 x 1


= 16 + 0  + 4 + 2 + 0


= 22


Therefore  ( 1 0 1 1 0 )₂ =  ( 22 )₁₀

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Problem 2: Convert ( 111000 )₂= ( ? )<sub>10


=  1 1 1 0 0 0</sub>
    ↑             ↑
MSB        LSB

= 1 x 2⁵ + 1 x 2⁴ + 1 x 2³ + 0 x 2² + 0 x 2¹+ 0 x 2⁰


= 1 x 32 + 1 x 16 + 1 x 8  + 0 x 4   + 0 x 2  + 0 x 1


= 32  +  16  +  8  +  0  +  0  +  0


= 56


Therefore  ( 1 1 1 0 0 0 )₂ =  ( 56 )₁₀

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Problem 3: Convert ( 010101 )₂= ( ? )<sub>10


=  0 1 0 1 0 1</sub>
    ↑             ↑
MSB        LSB

= 0 x 2⁵ + 1 x 2⁴ + 0 x 2³ + 1 x 2² + 0 x 2¹+ 1 x 2⁰


= 0 x 32 + 1 x 16 + 0 x 8  + 1 x 4   + 0 x 2  + 1 x 1


= 0  +  16  +  0  +  4  +  0  +  1


= 21


Therefore  ( 0 1 0 1 0 1 )₂ =  ( 21 )₁₀

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Problem 4: Convert ( 101 )₂= ( ? )<sub>10


=  1 0 1</sub>
    ↑      ↑
MSB    LSB

= 1 x 2² + 0 x 2¹+ 1 x 2⁰


= 1 x 4   + 0 x 2  + 1 x 1


= 4  +  0  +  1


= 5


Therefore  ( 1 0 1 )₂ =  ( 5 )₁₀

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Problem 5: Convert ( 01111 )₂= ( ? )<sub>10


=  0 1 1 1 1</sub>
    ↑          ↑
MSB       LSB

Here, zero at the beginning does not make any sense and we can safely eliminate the zero at the MSB position.


_{=  1 1 1 1}
    ↑       ↑
MSB    LSB


= 1 x 2³ + 1 x 2² + 1 x 2¹+ 1 x 2⁰


= 1 x 16 + 1 x 8  + 1 x 4   + 1 x 2  + 1 x 1


=  8  +  4  +  2  +  1


= 15


Therefore  ( 1 1 1 1 )₂ =  ( 15 )₁₀

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