Hello,
If you use resistors 4,3,2,1.1 you get the following total resistances. The hex code is the code that it takes to get that value. The values have been sorted so you can see the increments and they are not equal. The increments are shown on the far right. Note hex code 00 produces an open circuit because all switches are off, but you could add a permanent parallel resistor to get some lower value and not affect the other values too much unless it is a low value.
0.501901, 0F,
0.573913, 07, 0.072012
0.602740, 0B, 0.028827
0.670051, 0D, 0.067311
0.709677, 03, 0.039627
0.804878, 05, 0.095201
0.862745, 09, 0.057867
0.923077, 0E, 0.060332
1.100000, 01, 0.176923
1.200000, 06, 0.100000
1.333333, 0A, 0.133333
1.714286, 0C, 0.380952
2.000000, 02, 0.285714
3.000000, 04, 1.000000
4.000000, 08, 1.000000
inf, 00, inf
A better idea i think is to bite the bullet and use a 1 of 16 decoder and 16 'switches' and 16 hand selected resistances that range from 1 to 16 or really whatever you want. You could also have a second set of 16 resistors and switch them out or in with another switch. This would involve both N channel MOSFETs and P channel MOSFETs.
An even better way i think is to create a digital resistance decade box.
This would involve two 1 of 10 decoders, around 20 switches, and around 20 resistors. One set could go from say 0 to 9 Ohms in steps of 1 Ohm each and the second set from 10 to 90 Ohms in steps of 10 Ohms each (and one switch has to create 0 Ohms for that bunch too). That way you can get resistances from 0 to 99 ohms in steps of 1 Ohm each with an 8 bit binary word. You may have to make some adjustments in the resistor values for the 'on' state resistance of the transistors, but if you only have to go say 0 to 90 Ohms in steps of 10 Ohms and then 100 to 900 Ohms in steps of 100 Ohms then the transistor on state resistance may not matter as much. Again this would involve both N and P channel devices and perhaps some carefully planned drive circuits.
I could see something like this making a nice load box for testing power supplies and the like.
Another perhaps even more interesting idea would be to combine a current source with some known resistances. Since you can make a zero Ohm active current shunt this way, i would think you could create an 'any' Ohm shunt (which is just a resistor) this way too. It would take a decent voltage or current controlled current source and some control circuitry which may only require an op amp or two. If the resistances will only be used in a DC circuit this would be possible, but an AC version would have to be faster to response to fluctuations in the signal.
The main idea here is to make a larger resistor look lower or a lower resistor look higher in value by feeding the circuit a current from an external current source under the control of a measurement circuit.