The number 83 is written in the binary system as

Options

A. 100110
B. 101101
C. 1010011
D. 110110

Explanation

To convert the decimal number 83 into its binary representation, we can use the method of successive division by 2. Here’s a step-by-step solution:

### Step-by-Step Solution:

1. **Divide the number by 2**: Start with the number 83.
- 83 ÷ 2 = 41 with a remainder of 1.

2. **Continue dividing the quotient by 2**: Take the quotient (41) and divide it by 2.
- 41 ÷ 2 = 20 with a remainder of 1.

3. **Repeat the process**: Take the new quotient (20) and divide it by 2.
- 20 ÷ 2 = 10 with a remainder of 0.

4. **Continue dividing**: Take the new quotient (10) and divide it by 2.
- 10 ÷ 2 = 5 with a remainder of 0.

5. **Keep going**: Take the new quotient (5) and divide it by 2.
- 5 ÷ 2 = 2 with a remainder of 1.

6. **One more time**: Take the new quotient (2) and divide it by 2.
- 2 ÷ 2 = 1 with a remainder of 0.

7. **Final division**: Take the last quotient (1) and divide it by 2.
- 1 ÷ 2 = 0 with a remainder of 1.

8. **Collect the remainders**: Now, we collect all the remainders from the last division to the first. The remainders are:
- From last to first: 1, 0, 1, 0, 1, 1, 1.

9. **Write the binary number**: Therefore, the binary representation of the decimal number 83 is:
- **1010011**.

### Final Answer:
The number 83 in binary is **1010011**.