Answer 8
Some simple adjustments of the resistor values create equal-size voltage steps for the A/D converter as shown below.

This gives 5 V when no switch is pressed, and 0 to 3.75 V in approximately equal steps when a switch is pressed. This approach works well for up to 16 switches and beyond.

The general approach for calculating the resistor values is as follows:

1. Select the pull-up resistor value: 10 kilohms

2. Decide how many switches are required: N = 16

3. The top switch generates 0 V by shorting the A/D input to ground

4. The next switch down will generate V_CC/ n V:

5. Select the nearest standard 5% value: 680 ohms
6. Repeat for switches i = 2 through N – 1
a.The next switch down will generate,

You must subtract the values of the resistors above it
to helps avoid cumulative errors:

b. Select the nearest standard 5% value

For the specific example of 16 switches, you should end up with the following resistor values: 680, 750, 910, 1000, 1200, 1500, 1800, 2200, 2700, 3900, 5600, 7500, 13K, 27K, and 82K. Even with 5% resistors, all of the resulting voltages are within 0.25% of full scale of their nominal values.

Contributor: Dave Tweed

Published May 2003