There are several methods available to convert from base 10 to base 2. Let’s use two methods,** division** and **subtraction**, to convert the number 141_{10} to base 2. (Note the use of the subscript 10 (141_{10}) to denote the base used for the number.)

The** Division Method** uses the **remainder** when successively dividing by two to convert the number. For example:

- 141 divided by 2 is 70 remainder 1
- 70 divided by 2 is 35 remainder 0
- 35 divided by 2 is 17 remainder 1
- 17 divided by 2 is 8 remainder 1
- 8 divided by 2 is 4 remainder 0
- 4 divided by 2 is 2 remainder 0
- 2 divided by 2 is 1 remainder 0
- 1 divided by 2 is 0 remainder 1

We can then write down our new binary number simply by taking each remainder reading from the bottom up, so 141_{10} is **10001101 _{2}**

We can check this using our Base 2 table:

10001101_{2} is 128 + 8 + 4 + 1 = 141_{10}.

Decimal to Binary: What is 169 in base 2 (binary)? | Show |
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As you become more comfortable with the values of each binary column you can use the **Subtraction Method**.

- 141 contains one 128 leaving 13
- 13 contains no 64s
- 13 contains no 32s
- 13 contains no 16s
- 13 contains one 8 leaving 5
- 5 contains one 4 leaving 1
- 1 contains no 2s
- 1 contains one 1 leaving 0

We can then write this down as before as 10001101_{2}.

**Next: Binary to Decimal**