How To Convert Base 2 To Base 10

To convert base 2 to base 10 is similar in steps to converting other bases to base 10.

In this lesson, you will learn the step-by-step method for converting base 2 to base 10.

BONUS: A link to practice questions on number base is included at the end of this lesson.

Question on converting base 2 to base 10

Let’s take an example:

Question:

Convert 10010102 to a number in base 10

STEP 1.

Write out each digit in the base 2 number

1

0

0

1

0

1

0

STEP 2.

Put a multiplication sign and the base 2 in front of each digit

1 × 2

0 × 2

0 × 2

1 × 2

0 × 2

1 × 2

0 × 2

TAKE NOTE: (do NOT multiply yet)

STEP 3.

Starting with the last digit as ZERO, raise each base to the power of its position

1 × 26

0 × 25

0 × 24

1 × 23

0 × 22

1 × 21

0 × 20

STEP 4.

Calculate the “power” first (according to BODMAS)

1 × 64

0 × 32

0 × 16

1 × 8

0 × 4

1 × 2

0 × 1 (Law of Indices)

STEP 5.

Then multiply next

1 × 64 = 64

0 × 32 = 0

0 × 16 = 0

1 × 8 = 8

0 × 4 = 0

1 × 2 = 2

0 × 1 = 0

STEP 6.

Add your answers together

64 + 0 + 0 + 8 + 0 + 2 + 0 = 74

FINAL ANSWER:

1001010 (in base two)

= 74 (in base ten)

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Click the button to practice questions on number base.

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