In this two-part series, Martin Vlietstra will be looking at how digitisation is applied to measuring devices: In Part 1, he will examine what “digitisation” is and explain how it is applied to thermometers. In Part 2, he will look at how it is applied to weighing devices.
We regularly hear the term “digitisation”. I am not sure that everybody who uses the term fully understands what is meant by the term.
The term “digital devices” usually means that the device is controlled by a microprocessor (initially called “a computer on a chip”, now often called a microchip). Microprocessors first came into being in the 1970’s. The most successful early microprocessors were the Intel 8080 and Z80. These microprocessors formed the heart of the earliest personal computers including the Amstrad PCW. The Intel 8008 (predecessor to the Intel 8080) was first launched in 1972 with a price tag of $120. Today similar chips, when bought in bulk, cost $4 or less (without adjustment for inflation). Microchips, like their big brothers (computers), store numbers as a set of binary digits (often called bits). If the device concerned uses 8 bits to store its numbers, then it can store the numbers in the range 0 to 255 inclusive while a device that uses 10 bits can store number in the range 0 to 1023 (as shown below).
Many digital devices capture their information as an analogue value such as a voltage or an electrical current. These signals are then converted to a set of digital bits using a device called an analogue-to-digital convertor (ADC). As mentioned earlier, a microchip can be viewed as a “computer on a chip”. Although it can do many of the internal operations that a fully-fledged computer can do, it cannot add any accuracy to the input data. Note that extra decimal places do not improve the accuracy of the result.
As an example, we will look at how a digital thermometer works. When I bought one with an external probe a few years ago its specifications said that its operational range was from -50 °C to +50 °C (-58 °F to +122 °F). I analysed its operation carefully, first putting it in a plastic bag and immersing it in a bowl of icy water. It registered 0.0 °C (as expected) and when it was switched to Fahrenheit, it showed 32.0 °F (as expected). I then warmed the probe by placing it between my fingers and watched the temperature climb. When I switched it to the Celsius mode, the temperature climbed in 0.1 °C increments, but in Fahrenheit mode the increments were usually 0.2 °F, but were sometimes 0.1 °F. I then calculated the exact Fahrenheit conversion from degrees Celsius and compared my calculations to what was displayed. I found that the display rounded the exact conversion to the nearest 0.1 °F (and also silently propagated any conversion uncertainties).
From this I deduced the instrument was designed around a 10-bit ADC which gave a raw output in the range 0 to 1023. The conversions resulting from this output are catalogued below.
- Column 1: The values 0 to 1000 were generated by the instrument with 0 representing -50 °C and 1000 representing +50 °C. The remaining 23 values were not used.
- Column 2: A value of 500 was then subtracted from the digital reading to give a range of -500 to +500.
- Column 3: Since each increment represented an increase of 0.1 °C, the number is divided by 10 to get the temperature in degrees Celsius.
- Column 4: The temperature in degrees Celsius is converted to an exact value of degrees Fahrenheit.
- Column 5: The Fahrenheit values rounded to the nearest 0.1 °F.
The calculated values were found to be exactly the values that were observed – values not shown in Column 5 were not observed on the device.
The naive Fahrenheit user might think that since he sometimes gets an odd number and sometimes gets an even number on the Fahrenheit display, the Fahrenheit value is more accurate than the Celsius value. However, a careful examination of all the Fahrenheit values shows that consecutive five values have an even number in the decimal place (31.6 °F to 32.4 °F – shown in blue) followed by five odd numbers in the decimal place (32.5 °F to 33.3 °F – shown in red). This pattern then repeats itself. In short, the thermometer was designed to display degrees Celsius and the Fahrenheit display was a “cheap add-on”.
In high accuracy work, users would expect the increments to be consistent. In the case of displaying degrees Fahrenheit, this would entail using a second 10-bit ADC which is tuned to have increments of 0.2 °F. This would result in a more expensive instrument which, for the domestic market at any rate, would not be acceptable, so the manufacturers hide this discrepancy by not publishing the specifications in full.
https://en.wikipedia.org/wiki/Analog-to-digital_converter
https://en.wikipedia.org/wiki/Microprocessor
https://en.wikipedia.org/wiki/Binary_number
https://en.wikipedia.org/wiki/Digital_signal_processor
Image of thermometer is courtesy of User: JePe from Wikimedia Commons.
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