1. **Problem Statement:** We are given a table with hexadecimal values and corresponding decimal values, and we need to find the formula or relation connecting them and predict the missing hexadecimal value for the decimal 100000000. 2. **Observing the Data:** The table shows three columns: a hexadecimal number, a decimal number, and another hexadecimal number, followed by a decimal value. The pattern suggests the second column is decimal, the first and third columns are hexadecimal representations related to the decimal number. 3. **Hexadecimal Patterns:** The third column appears to be hexadecimal numbers of the form $1f$, $3f$, $7f$, $ff$, $1ff$, $3ff$, $7ff$, $fff$, $1fff$, $3fff$, $7fff$, $ffff$, $1ffff$, $3ffff$, $7ffff$, $fffff$, $1fffff$, $3fffff$, $7fffff$, $ffffff$, $1ffffff$, $3ffffff$, $7ffffff$, $fffffff$, $1fffffff$, $3fffffff$, $7fffffff$, $ffffffff$, $1ffffffff$, $3ffffffff$, $7ffffffff$, $ffffffff$. 4. **Relation Between Decimal and Hex:** The decimal numbers are powers of 2 multiplied by 1000 or exact powers of 2, and the third column hex values correspond to $2^n - 1$ for some $n$. 5. **HTA Formula:** The question mentions "hta formula" which likely refers to a formula relating these values. The third column hex values are of the form $2^n - 1$ where $n$ is the number of bits. 6. **Predicting the Missing Value:** For decimal 100000000, the third column is $1ffffffff$ (hex). The first column is missing (marked as '?'). 7. **Finding the First Column:** The first column seems to be the hexadecimal representation of the decimal number in the second column. 8. **Convert 100000000 to Hex:** Convert decimal 100000000 to hexadecimal: $$100000000_{10} = 5F5E100_{16}$$ 9. **Answer:** The missing value '?' is $5f5e100$. **Final answer:** The missing hexadecimal value corresponding to decimal 100000000 is **5f5e100**. This matches the pattern of the first column being the hexadecimal representation of the decimal number in the second column.