# What does a half-digit mean in case of accuracy?

What does it mean when somone says something like "3 and 1/2 digit" in case of accuracy of test equipments (or maybe A/D converters?) Can somone explain this a bit with some numbers as examples?

3 digits would be 0 through 999
3 1/2 digits is 0 through 1999 (typical for DMMs)
3 3/4 digits is typically 0 through 3999

Has nothing to do with binary digits, but decimal digits, or rather their representation in 7-segments displays. To display every digit you need all 7 segments, but if for the fourth digit you only have to display a "1" you only need the two rightmost segments, so that can be interpreted as the right half. That was when most DMMs had a maximum reading of 1999. Recently more accurate DMMs became available, having readings up to 3999. If "1" as the highest value for the highest order digit is half a digit, with some imagination you could say that a highest value of "3" is 3/4 of a digit.

Note that for displaying only "1", "2" and "3", you don't need the upper left segment, which a 3 3/4 digit DMM indeed doesn't have for the leftmost digit. It's a small cost saving, but a saving nevertheless.

• Thanks, So is that 1/2 or 3/4 has something to do with MSB? why 1/2 is 0 or 1? and 3/4 is 0 to 3? Commented Sep 20, 2011 at 10:07
• @Seaņ - added to my answer. Commented Sep 20, 2011 at 10:18
• Incidentally, see blogs.msdn.com/b/ericlippert/archive/2005/01/12/… for an interesting and relevant observation: if one picks a physical quantity at random, the first digit is more likely to be a 1 than either a 2-3, and almost as likely to be in the range 1-3 as in the range 4-9. Commented Mar 1, 2012 at 21:17
• @supercat As a bonus from your reference I see that IF you exclude values 0 & 1 then all other positive binary numbers can be written with their left most digit truncated. eg 1011 can be safely represented by 011. How to deal with 0 & 1, and what practical use may be made of this 'fact' are TBD :-). Commented Apr 7, 2014 at 12:42
• @RussellMcMahon: That assumption only holds if the exponent is variable. On many meters, it's useful to be able to lock the exponent (e.g. if reading signals that are between 1 and 3 volts, one may wish to stay on the 19.99 range); for that to work, the leading digits must be viewed as significant. Commented Apr 7, 2014 at 15:09

David L. Jones did a video about Multimeter Counts, Accuracy, Resolution & Calibration.

There he also explains what these half digits are.

To summarize his explaination what 3 1/2 digits mean (in the video 0:30 - 1:30):

A 3 1/2 digits meter can display 1999.

A 4 1/2 digit meter can display 19999 and so on.

The half means that the most significant digit can only go up to 1.

• David L Jones may have created a video, but you've created a post on the Electrical Engineering Stackexchange! Please make sure to summarize any reference materials in your answer to the question. This is especially true with videos; some users won't have (1) a place to listen to the video, (2) time to watch the video, or (3) an accurate link (in the future, if your link expires). Please make all answers as self-sufficient as possible. Thank you! Commented Sep 20, 2011 at 10:24
• @Kevin Vermeer: You are right. I'm sorry. I have summarized the part that is relevant to the question. I also added the time, so one doesnt have to watch the whole video. Next time I will add all the content in the first place. Commented Sep 20, 2011 at 11:51
• Thanks, this was a nice explanation. I wonder how I missed this video of Dave. His only problem is that there are no good search and indexing on his site :P Commented Sep 21, 2011 at 7:06
• @Sean87 You are so right. I realy love his tutorials, but sometimes they are hidden in a product teardown video or something else. The first time I skipped these videos ^^ Commented Sep 21, 2011 at 8:52
• @Kevin You really know what you are talking about! I was just in university library and couldnt hear dave because there were no speakerss connected to PC (Or even it had no sound card!) Commented Sep 21, 2011 at 9:16

My best guess with this is that it is in reference to LCD or LED displays.

Some test equipment may well have a "3½ Digit" display. That is, a display with 3 whole digits, and only half of the fourth digit (i.e., a "1").

So the full range of a 3½ digit display would be:

0 to 1999

All segments on would give you:

1888

Take this one as an example:

That one's from a 12-hour clock, so there is never any need for the first digit to ever go above 1.

This is a useful marketing term used to explain the nature of a digital display.

It means that the most significant digit can be either 0 or 1.
A 3 digit numeric display can display numbers from 000 to 999. A 3.5 digit display displays numbers from 000 to 1999 or twice as much.

By adding a relatively low cost display to the system the manufacturer doubles the displayed range. This results in eg multimeters with 2, 20, 200 Volt or mA ranges rather than 1, 10, 100, 1000 ranges. Note that on a 3.5 digit display multimeter the max range on AC volts may be eg 600 Volts rather than the possible 1999 Volts. This is a safety and implementation limitation.

The 3 or 3.5 digit display does not affect the accuracy - but it does affect the displayed apparent resolution. Note that most multimeters have absolute accuracies typically around 1% to 2% on Volt and mA ranges and worse on ohms and Amp ranges. This despite the fact that a 3 digit display has a 0.1% resolution and a 3.5 digit display has a 0.05% resolution. In such cases adding the extra resolution can be useful even though the accuracy is already more than outstripped by the display resolution.

Rarely you may see 3 + 3/4 digit meters - these have eg 0000 to 2999 resolution. This can be extremely nice to have. It gives eg 4, 40, 400, ... ranges. My experience with these is that it often eliminates range changing in typical use when maximum resolution is required with a widely varying signal. These are very seldom seen.

• Actually, 3-3/4 digit displays have become quite common. I just bought a very nice brand-new auto-ranging Victor VC921 multimeter on eBay for US$13.20, shipped to my door, and it has 3-3/4 digits of precision for voltage, resistance & capacitance. Commented Apr 7, 2014 at 3:34 As noted, the term "3 1/2 digit" was coined some time ago to refer to displays that could show three digits 0-9, and a leading digit which could be blank or 1. When some later displays came along with a leading digit that could display 0-2 or 0-3, the terms "3 2/3 digit" and "3 3/4" digit were coined. Note that were it not for the earlier usage of "3 1/2" digit, it would perhaps be more accurate in terms of magnitude to say "3 1/3" digit for leading 0-1, "3 1/2" digit for leading 0-2, and "3 2/3 digit" for 0-3, since log10(2000) is 3.3, log10(3000) is 3.5, and log10(4000) is 3.6, but the terms are what they are. BTW, a 3 2/3 digit display needs three controllable segments for the left digit (the upper-right segment, the lower-right, and everything else that makes up a "2"); a 3 3/4 digit display needs four controllable segments (upper-right, lower-right, lower-left, and all three verticals). Counting up to 4 would require five segments (split out the middle one), 5 would require six (add the upper left), and seven would require all seven (split the top from the bottom). All the other answers here are talking about decimal digits on displays. For A/D converters the meaning of accuracy is totally different and is usually given as a fraction of an LSB (least-significant bit), which means that the value of the conversion is accurate to within that numerical amount. This is also captured in the ENOB (effective number of bits) which is also a fractional number -- for instance, an "8-bit" A/D converter will probably only have an ENOB of around 7 bits. The reason the number can be fractional is due to several things. If it was only due to quantization, and all else was perfect, all conversions would be accurate to 0.5 bits. The reason it's not exactly that is due to other effects such as conversion non-linearity and distortion. Reading up on ADC terms more may help. In addition, the cost of the A/D converter is exponential with additional bits. You can scale the input, to read 2V, 20V, 200V etc, but with 10 bits, 0-1023, you only ever get approx 3 digits of accuracy: 000 -- 999. So what you get on a 10 bit, general purpose multi-meter is approximately 3 digits of accuracy. You can scale that 0.999, 1.998, 3.996, 8.992, or to any intermediate value, but as you add extra range at the top, you loose accuracy in the bottom digit. If you drop the bottom digit, you lose information: that bottom digit '8' may be plus or minus '4', but if you don't show it at all, it's plus or minus '9'. Because it's generally useful, the bottom digit was often scaled to +/- 0.5. That is, a reading of 1.999 means 1.999 +/- 0.0005 -- which is 10 bits of resolution. So 3 1/2 digits means 10 bits, and 10 bits gives 3 1/2 digits. Better meters sometimes have 11 bits, 3.999 full scale +/- 0.0005, or 12 bits, 9.999 (Yes, if you scale to 9.999 instead of 7.999 you aren't as accurate on the last digit, but that last bit is difficult anyway, and the last digit is probably +/- 0.001 on a 12-bit bench meter.) • However, it's trivial to get ADCs with much higher resolution than 10 bits, because a multimeter doesn't need the extreme speed of flash ADCs, the only type that follows the exponential trend you claim. You can get delta-sigma ADCs up to 24 bits for about$10, definitely affordable enough to put in a multimeter you're going to sell for $300 or$400. Useless for an oscilloscope, but a multimeter only needs a few samples per second, and the ones I see on digikey for under $10 offer up to a few thousand samples per second. Commented Feb 25, 2022 at 2:04 • Now, flash ADCs, the really fast ones, are indeed extremely expensive to get at high bit depth. Again going just by what digikey has available (because I can't be bothered to look into it much further right now), up to 16 bit flash ADCs are available, but you pay through the nose for those sixteen bits; they start at$130 and go up from there. Commented Feb 25, 2022 at 2:07