The resistors are used to provide a pull-down function to prevent the outputs which are not connected to Vdd (via the various diodes) from floating. As you might be aware, if inputs to an IC, for instance CMOS 4000-series or 74HC-series, are left floating, all manner of unpredictable behavior may occur.

 

The circuit shown is not really an "encoder" per se, it's really a decimal to binary converter, using a diode matrix.

 

Reread post #2. All is explained there.

My suggestion: draw the circuit twice but only for the positions 3 and then 7, for example, so you can compare.

See what happens where there is a resistor and where there isn't.

 

The existing resistors ARE connected to points 1,2, and 4.

Les.