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The 3456a was the most accurate in the HP fleet when introduced in 1981. The model line was 345x, so in its heritage was the 3455, 3457, and finally the ersatz standard DMM today, introduced in ~1989, the 3458. HP introduced a high accuracy ADC method, multislope II, with 3456a, you'll see marked change in posted accuracy versus the 3455a. The 3458a further improves that technique. In summary, if you're looking for accuracy these series of DMMs are one to shoot for.

There are pros and cons to the discontinued models, 56a and 57a. For example, The 56a is as good as the 57a in DCV at 1 year ppm, while the 57a is 10x more stable in 1yr as a ohmmeter. The 57a uses all close case calibration and has more unobtanium in its parts list, versus the 56a, which was the last to use all pots based calibration. The basic 57a reads only to 300Vrms maximum, but also has a current mode.

As for prices, the low end is similar on both, about $50 without shipping, but on the high end with calibration, the 56a runs to $300 while 57a about $700.

The 3478a was a general purpose working meter, ~10x less accurate in DCV than the 3456a.

As mentioned earlier you can use a resistor network; dekaviders or KV bridges in DC, to generate other DC voltages needed to check ranges, but maintaining stability in the reference enough to check the meter's accuracy, is the challenge. Its enough a whole new forum discusses this issue alone, volt-nuts@.... A similar problem exists for AC.

To calibrate a meter to realize its best accuracy requires grasping key concepts in metrology. A simplest approach is to take your DMM and compare its readings against a known good DMM. The reference DMM should ideally be 4x to 10x more accurate than the DUT. This is the concept of TUR, test uncertainty ratio. When making comparisons, say voltages, the test volt must be stable and precise enough during the transfer, for example if you are checking the 1V range between DMMs, you need to generate a 1V voltage stable to 1uV resolution or less, 1.000 000 VDC. Without a high level of thoroughness and stability, your 6.5 digit DMM will have increasing uncertainty as you get to its LSD.

On the low end of the range, special conditions apply that are fully covered in Keithley's low level measurement handbook, and these need to be controlled once dealing with uV, mohms, and uA adjustments.

Lastly, one has to decide if the effort described in volt nuts is worth it, or should one just take your DUT to the calibrator periodically for $100-$150 to insure your 6.5 digit DMM is as good as you expect it to be.