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Understanding the Formula Works: BASE(SUMPRODUCT(...))

In this article, we will discuss the formula BASE(SUMPRODUCT(B32:Y32=“1”,2^(33-COLUMN(B32:Y32))),16), which takes content from 24 cells in a single row, and performs a calculation based on those cells.

The formula consists of two main parts: SUMPRODUCT(...) and BASE(...). Let's break down each part and understand how they work together.

SUMPRODUCT(...)

The SUMPRODUCT(...) function is a powerful tool in Excel that allows you to perform complex calculations on multiple ranges of cells. In this case, it is used to find the sum of a series of products.

The first argument of SUMPRODUCT(...) is the comparison between the cells in the range B32:Y32 and the string “1”. This comparison returns an array of TRUE and FALSE values, where TRUE indicates that the cell contains “1”.

The second argument of SUMPRODUCT(...) is the expression 2^(33-COLUMN(B32:Y32)). This expression calculates the powers of 2, starting from 2^33 and decreasing by 1 for each column, from B32 to Y32. The COLUMN(...) function is used to get the column number of each cell in the range.

The SUMPRODUCT(...) function then multiplies each pair of values from the two arrays and sums the results. This gives us a sum of products, where each product is the result of multiplying a TRUE or FALSE value by a power of 2.

BASE(...)

The BASE(...) function is used to convert a number from one base to another. In this case, it is used to convert the sum of products from binary (base 2) to decimal (base 10).

The first argument of BASE(...) is the result of the SUMPRODUCT(...) function, which is a binary number. The second argument of BASE(...) is the base we want to convert to, which is 16 in this case.

Summary

In summary, the formula BASE(SUMPRODUCT(B32:Y32=“1”,2^(33-COLUMN(B32:Y32))),16) takes content from 24 cells in a single row, and calculates a decimal number from the binary number represented by the sum of products of the TRUE or FALSE values and the powers of 2.

References

• Microsoft Excel Help: SUMPRODUCT function
• Microsoft Excel Help: BASE function
• Exceljet: SUMPRODUCT function with multiple criteria
• Chip Pearson's Excel Tips: SUMPRODUCT with multiple criteria