The image shows a binary floating-point number with the format:

• Sign bit: 0 (positive)
• Exponent: 10000010
• Mantissa: 1.11000000000000000000000

This follows the IEEE 754 single-precision floating-point format.

Steps to decode:

1. Sign bit: 0 means the number is positive.

2. Exponent: 10000010 in binary translates to 130 in decimal. The exponent in IEEE 754 is stored with a bias of 127, so the actual exponent is: $130 - 127 = 3$

3. Mantissa: The mantissa is given as 1.11000000000000000000000. In IEEE 754, the leading 1 is implicit, so we interpret the mantissa as: $1 + 0.5 + 0.25 = 1.75$

4. Putting it all together: $\text{Value} = (-1)^{\text{sign}} \times 1.75 \times 2^{3}$ $\text{Value} = 1.75 \times 8 = 14$

So, the decimal equivalent of this binary floating-point number is 14.

Would you like further details or explanations?

Here are 5 related questions:

1. How does IEEE 754 handle denormalized numbers?
2. What is the role of bias in floating-point representations?
3. How are floating-point numbers compared for equality in binary systems?
4. What is the smallest and largest number that can be represented using single-precision IEEE 754 format?
5. How does rounding affect floating-point calculations in practical applications?

Tip: Understanding how floating-point numbers are stored and interpreted can help avoid precision errors in calculations, especially in programming.