Convert `(128)_(10)` into binary system.

Answer

To convert the decimal number \( (128)_{10} \) into binary, we can follow these steps:

### Step-by-Step Solution:

1. **Divide the number by 2**: Start by dividing the decimal number (128) by 2.
\[ 128 \div 2 = 64 \quad \text{(Remainder: 0)} \]

2. **Continue dividing the quotient by 2**: Take the quotient (64) and divide it by 2.
\[ 64 \div 2 = 32 \quad \text{(Remainder: 0)} \]

3. **Repeat the process**: Continue this process with the new quotient (32).
\[ 32 \div 2 = 16 \quad \text{(Remainder: 0)} \]

4. **Keep dividing**: Divide the next quotient (16) by 2.
\[ 16 \div 2 = 8 \quad \text{(Remainder: 0)} \]

5. **Continue dividing**: Now divide 8 by 2.
\[ 8 \div 2 = 4 \quad \text{(Remainder: 0)} \]

6. **Divide again**: Divide 4 by 2.
\[ 4 \div 2 = 2 \quad \text{(Remainder: 0)} \]

7. **Final division**: Finally, divide 2 by 2.
\[ 2 \div 2 = 1 \quad \text{(Remainder: 0)} \]

8. **Last quotient**: Now divide 1 by 2.
\[ 1 \div 2 = 0 \quad \text{(Remainder: 1)} \]

9. **Collect the remainders**: Write down the remainders from the last division to the first.
- The remainders are: \( 1, 0, 0, 0, 0, 0, 0, 0 \).

10. **Write the binary number**: Reading the remainders from bottom to top gives us the binary representation.
\[ (128)_{10} = (10000000)_2 \]

### Final Answer:
The binary representation of \( (128)_{10} \) is \( (10000000)_2 \).