The binary number expression of the decimal number 31 is:

Options

A. 1111
B. 10111
C. 11011
D. 11111

Answer

To convert the decimal number 31 into its binary number expression, we will use the method of repeated division by 2. Here are the steps:

### Step-by-Step Solution:

1. **Divide the number by 2**: Start by dividing 31 by 2.
- Quotient: 15
- Remainder: 1

2. **Continue dividing the quotient by 2**: Now take the quotient (15) and divide it by 2.
- Quotient: 7
- Remainder: 1

3. **Repeat the process**: Take the new quotient (7) and divide it by 2.
- Quotient: 3
- Remainder: 1

4. **Continue dividing**: Take the quotient (3) and divide it by 2.
- Quotient: 1
- Remainder: 1

5. **Final division**: Now take the quotient (1) and divide it by 2.
- Quotient: 0
- Remainder: 1

6. **Collect the remainders**: Now, we will collect all the remainders from the last division to the first. The remainders are: 1, 1, 1, 1, 1.

7. **Write the binary number**: Reading the remainders from bottom to top gives us the binary representation of 31, which is 11111.

### Final Answer:
The binary number expression of the decimal number 31 is **11111**.