A. There are a few potential issues causing your extremities to go numb or have that "tingling" feeling. The most basic and obvious culprit is pressure on a nerve which causes the numbness due to constriction of the pathway of the nerve impulses.
The Stationary Bike
Generally "spinners" find this happening when they put too much pressure on the handlebars. With the wrist flexed and direct pressure the nerve(s) you can receive enough pressure to inhibit the pathway of the nerve. This can be minimized by frequently adjusting your hand placement, raising the handlebar to prevent forward lean on the bar or wearing cycling gloves which have padding. Have a Certified Spin Instructor assist with proper settings for your bike.
If you find your neck or shoulders are going numb, chances are the biomechanics are not proper. Your seat and/or handlebars may not be aligned properly. This is not only true for spin bikes but stationary and road bikes as well.
The Elliptical Trainer
The feet going numb is a common issue when using the elliptical. This is because your feet stay in a relatively fixed position with flexion taking place at the ball of the foot. Since you don't push off your foot as you would on a treadmill when walking or running, the nerves on the bottom of the foot receive direct pressure. Make sure your shoes fit properly and the laces aren't too tight. Adjusting your foot placement occasionally and changing pedal direction should also help minimize your feet from going numb. Try to minimize being on the balls of the feet and roll from the balls of your feet to the heels as well.
*If you find these simple adjustments are not effective, consult your physician.