The image you provided contains two decimal numbers: 4.344 and 5.511. It seems like the task is related to converting these decimal numbers to their binary equivalents. Here's how you can convert each of these decimal numbers to binary:

Step-by-Step Conversion

1. Convert the integer part to binary:

• For 4: $4 \div 2 = 2 \text{ remainder } 0$ $2 \div 2 = 1 \text{ remainder } 0$ $1 \div 2 = 0 \text{ remainder } 1$ So, 4 in binary is 100.

• For 5: $5 \div 2 = 2 \text{ remainder } 1$ $2 \div 2 = 1 \text{ remainder } 0$ $1 \div 2 = 0 \text{ remainder } 1$ So, 5 in binary is 101.

2. Convert the fractional part to binary:

• For 0.344: Multiply by 2 and take the integer part each time: $0.344 \times 2 = 0.688 \quad (\text{integer part } = 0)$ $0.688 \times 2 = 1.376 \quad (\text{integer part } = 1)$ $0.376 \times 2 = 0.752 \quad (\text{integer part } = 0)$ Continue this until you have the desired precision. The binary fractional part starts as 0.01011...

• For 0.511: Multiply by 2 and take the integer part each time: $0.511 \times 2 = 1.022 \quad (\text{integer part } = 1)$ $0.022 \times 2 = 0.044 \quad (\text{integer part } = 0)$ $0.044 \times 2 = 0.088 \quad (\text{integer part } = 0)$ Continue this until you have the desired precision. The binary fractional part starts as 0.100...

Final Binary Representation:

• 4.344 ≈ 100.01011...
• 5.511 ≈ 101.100...

Would you like a more detailed explanation or further calculations? Let me know if you have any questions!

Follow-Up Questions:

1. How can you convert binary fractions back to decimal?
2. What is the significance of repeating patterns in binary fractions?
3. How does the binary number system relate to computer memory?
4. How would you convert a larger decimal number to binary?
5. What is the difference between floating-point and fixed-point binary representations?

Tip:

When converting decimal fractions to binary, the process is iterative and can result in repeating binary digits. It’s often helpful to set a limit on the number of binary places for practical use.