Math Encounters Blog

Quote of the Day

Courage is not the absence of fear, but rather the assessment that something else is more important than fear.

— Franklin Delano Roosevelt

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Figure 1: Simplified Version of the DAC Table.

I was recently given a specification for a Digital-to-Analog Converter (DAC) that contains a table of register settings that correspond to the DAC's output voltage. Each row of the table corresponds to one register setting and each register column corresponds to a register bit. Thus, each table cell corresponds to a single bit – a 1 or 0. A simplified version of this table is shown in Figure 1 – a simplified version of the much larger table I was working with.

I wanted to convert the table's binary settings to hexadecimal for ease of programming. As I looked at the table, it became apparent that converting these binary values to hexadecimal will allow me to showcase some of Power Query's list processing capabilities.

In this exercise, I will show to use Power Query to

• Convert the binary columns to a decimal value
• Convert the decimal value to hexadecimal

I like this example because it is short and easy to follow. I use this example in my Excel tutoring to illustrate the use of lists and records. My workbook containing the m-code is here. Please refer to the workbook for the details. Below, I discuss a couple of points that people sometimes find confusing.

Background

Convert Binary to Decimal

Before going forward, it is important to understand the data types associated with a Power Query table:

• Columns are lists
• Rows are records
• You address a subset of the cells in a single table row using the syntax
  table_name{row_number}[[col1], [col2], ..., [coln]]
• This subset will have a data type of record.

The following formula is used in the Excel workbook to generate a decimal number from the individual binary digits.

Convert Binary to Hex

There are a couple of ways to perform binary-to-hex conversion. The approach here uses Power Query's Number.ToText function to perform the conversion.

Result

The workbook outputs the following table.

I have used this approach for converting numerous binary tables to hex form. This approach also provides a nice illustration of how to use the list.accumulate function.

Quote of the Day

If you haven't read hundreds of books, learning from others who went before you, you are functionally illiterate – you can't coach and you can't lead.

— Jim Mattis, scholar general

Figure 1: Glass-Encased Fuse. (Wikipedia)

I have been analyzing seemingly random fuse failures in different products. The failing fuse is similar to the unit shown in Figure 1. My analysis has shown that the fuses are failing because of damage they are sustaining during the manufacturing process. In my analysis report, I was asked to list each product that experienced a fuse failure and to list how many days each product was in service before the fuse failure occurred. Because of the large number of products and failures, I wanted to find a table format that would contain the required information in a condensed format. Excel's TEXTJOIN function and pivot table feature solved my problem nicely. For confidentiality and presentation reasons, my example here will contain simulated failure data that is MUCH shorter than the actual data file.

Figure 2 shows an abbreviated version of my test results table that contains the RMA number, failed assembly name, and the number of days the assembly was in service. I appended a column to this table that contains the Excel function:

=TEXTJOIN(",",TRUE,IF(C17=[Assembly],[Days in Service],""))

This function creates a comma-separated values list of all the "Days in Service" values associated with the failed assemblies. I then used a pivot table to generate my final summary table. The entire process is shown in this Excel workbook, which contains a macro from the Contextures web site that turns off the filter arrows.

Figure 2: Illustration of My Table Transformation.

Quote of the Day

Gratitude is riches. Complaint is poverty.

— Doris Day. This quote is another expression of the Benedictine philosophy.

Figure 1: Yellow highlight shows the function output for the number list shown.

While working on a test report for an aircraft manufacturer this week, I needed to convert a large number of number lists to strings of dashed ranges. For illustration, suppose you are given a list {1, 2, 3, 5, 6, 7, 8, 10}. Converting this list to a dashed set of ranges means generating the string "1-3, 5, 6-8, 10." Figure 1 shows another example with an optional prefix added to each number.

The need for this operation is more common than you might think. I usually see the dashed string format used on Bills of Materials (BOMs) for listing out the reference designators for specific part numbers, like resistors. A PCB BOM might have multiple 10Ω resistors with reference designators listed as "R1-R3, R5, R6-R8, R10." Normally, the schematic capture system would generate the reference designators in this format automatically, but I have worked in situations where the parts lists were in Excel and you needed to convert lists to list of dashed ranges.

Today's situation involved creating a dashed range list of the various graphs in a test report that had calibration and data charts interspersed. The customer wanted their data formatted this way and I complied – the life of a contractor.

My workbook is attached here. The VBA code is shown below.