hi Mark,
Which Binary selector switch did you final buy.??
Its important, the circuit is drawn to suit a /1,/2,/4,/8 output with the common on the switch to 0V.
So when say position '1' is selected on the switch, only the pin#4 on the CD4516 is High [+v] and the other 3 pins, 12, 13, 3, are Low [0v]
Example 2: switch position #7, CD4516 pins 4,12,13 should be High [+v] and pin 3 Low [0v]
Use a voltmeter, select position #1 on the Binary switch and measure the voltages on the parallel input pins of the CD4516, lets know what you have.