How To Convert Base 10 To base 2

Converting from base 10 to base 2, or to any other base, requires the use of a method called “repeated division.”

In this lesson, you will learn the step-by-step method of using repeated division to convert base 10 to base 2.

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

Question on converting base 10 to base 2

Let’s take an example:

Question:

Convert 7410 to a number in base 2

STEP 1.

Draw a table that looks like “T”

STEP 2.

Put the base 2 the TOP LEFT side of your table

2

STEP 3.

Put the base 10 number on the TOP RIGHT side of your table

274

STEP 4.

Divide the base 10 number by the base 2

274

STEP 5.

Write your result under the base 10 number

274
37

STEP 6.

Write the remainder in front of your result

274
37 remainder » 0

STEP 7.

Repeat step — 4, 5, 6 for every result until your result is less than base 2

274
237 remainder » 0
218 remainder » 1
29 remainder » 0
24 remainder » 1
22 remainder » 0
1 remainder » 0

STEP 8.

Once your result is less than base 2, write ZERO as your next result

274
237 remainder » 0
218 remainder » 1
29 remainder » 0
24 remainder » 1
22 remainder » 0
21 remainder » 0
0

STEP 9.

Put your last result as the last remainder

274
237 remainder » 0
218 remainder » 1
29 remainder » 0
24 remainder » 1
22 remainder » 0
21 remainder » 0
0 remainder » 1

STEP 10 — final answer

Write out the remainders from the BOTTOM to the TOP

= 1001010

FINAL ANSWER:

74 (in base ten)

= 1001010 (in base two)

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Otherwise,

Click the button to practice questions on number base.

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