The binary number expression of the decimal number 31 is

Options

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

Explanation

To convert the decimal number 31 into its binary expression, 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 decimal number 31.
- \( 31 \div 2 = 15 \) with a remainder of **1**.

2. **Divide the quotient by 2**: Take the quotient from the previous step (15) and divide it by 2.
- \( 15 \div 2 = 7 \) with a remainder of **1**.

3. **Repeat the process**: Continue dividing the quotient by 2.
- \( 7 \div 2 = 3 \) with a remainder of **1**.
- \( 3 \div 2 = 1 \) with a remainder of **1**.
- \( 1 \div 2 = 0 \) with a remainder of **1**.

4. **Collect the remainders**: Now, we collect all the remainders from the divisions, starting from the last division to the first.
- The remainders collected are: **1, 1, 1, 1, 1**.

5. **Write the binary number**: The binary representation of the decimal number 31 is obtained by reading the remainders in reverse order.
- Therefore, the binary expression of the decimal number 31 is **11111**.

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