Question

Convert decimal 165 into binary​

Answer 1

Write 165 as a sum of powers of 2 :

165 = 128 + 37

165 = 128 + 32 + 5

165 = 128 + 32 + 4 + 1

165 = 2⁷ + 2⁵ + 2² + 2⁰

This translates immediately into the decimal expansion of a binary number,

165 = 1×2⁷ + 0×2⁶ + 1×2⁵ + 0×2⁴ + 0×2³ + 1×2² + 0×2¹ + 1×2⁰

so that

165₁₀ ≡ 1010 0101₂

Answer 2

10100101₂

Explanation:

• To convert decimals to binary, you have to divide the decimal by 2 until it meets zero.
• Also, while dividing the number by 2 you have to write the remainder in each step.
• And then you have to write the remainders from bottom to top.

Let us solve it now.

2 |165

2 |82 - 1

2 | 41 - 0

2 |20 - 1

2 |10 - 0

2 | 5 - 0

2 |2 - 1

2 | 1 - 0

0 - 1

Now write the remainders from bottom to top.

165 = 10100101₂