Usually we convert a number from a given base to base 10 by multiplying every digit in the given number with the corresponding power of its base and then adding all these products:
For ex: To Convert 1011₍₂₎ to base 10, we do it as
1×2³ + 0×2² + 1×2¹ + 1×2⁰ = 8+0+2+1 = 11

As you can see here, using higher powers becomes difficult once the number of digits gets bigger and also as the base is larger (For ex: base 16)

A more simple approach for this would be Horner’s Algorithm.

Horner’s Algorithm is used to convert a number from a given base system to base 10 System.
The Steps involved in this conversion process are as follows.

• Take The First Digit of the given number
• Multiply it with it’s base and add the next digit in the number to this product
• Repeat the above step till all the digits are done and you have the base 10 value of the number

For instance: Consider 1011₍₂₎. Now to convert this to base 10 using the above method.

1. Take 1 i.e. the first digit in the given number.
2. Multiply it by 2 i.e. the given base. So we have 1×2=2.
3. Add the next digit i.e. 0 to this product. So we have 2+0=2.

Repeat the steps 2 and 3 as follows:
2×2=4 Then 4+1=5
5×2=10 Then 10+1=11

11 is the base 10 value of 1011₍₂₎.

This procedure of conversion could be simplified if you write it down as follows.

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