Question

What is 10 in binary code?

Answer 1

To convert the decimal number 10 to binary code, you need to express it in base-2 numeral system, which uses only the digits 0 and 1. Here’s a step-by-step explanation of how to do this conversion:

1. **Find the Largest Power of 2 Less Than or Equal to 10:**
   - The powers of 2 are: \(2^0 = 1\), \(2^1 = 2\), \(2^2 = 4\), \(2^3 = 8\), \(2^4 = 16\), etc.
   - The largest power of 2 less than or equal to 10 is \(2^3 = 8\).

2. **Subtract This Power of 2 from 10:**
   - \(10 - 8 = 2\)
   - Now, you need to represent 2 in binary.

3. **Find the Largest Power of 2 Less Than or Equal to 2:**
   - The powers of 2 are: \(2^0 = 1\), \(2^1 = 2\)
   - The largest power of 2 less than or equal to 2 is \(2^1 = 2\).

4. **Subtract This Power of 2 from 2:**
   - \(2 - 2 = 0\)
   - The remainder is 0, so you’re done with the conversion.

5. **Write the Binary Representation:**
   - To write the binary representation, you place 1s in the positions corresponding to the powers of 2 used, and 0s in the positions not used. For 10, the positions are \(2^3\) and \(2^1\):
     - \(2^3\) (8) → 1
     - \(2^2\) (4) → 0
     - \(2^1\) (2) → 1
     - \(2^0\) (1) → 0
   - Therefore, 10 in binary is written as \(1010_2\), where the subscript \(2\) indicates that this number is in base-2.

So, the binary representation of the decimal number 10 is \(1010\).

Answer 2

In binary code, the number 10 is represented as `1010`. This is based on the binary system, which uses only two digits: 0 and 1. Each position in a binary number represents a power of 2, starting from the right with 2^0. For the number 10:

- 2^3 (8) + 2^1 (2) = 10
- So, 10 in decimal is `1010` in binary.