A variable flow rate gas control valve for use in consumer and commercial appliances is presented. The valve utilizes two or more solenoids to control the operating position of two different valve members whose orifices are sized in an exponential relationship with one another. By opening one or more of the valving members in various combinations, a variable flow rate of gaseous fuel may be controlled in integer multiple steps from full off to full on. The solenoid configurations may be in line, opposing, or symmetrical about an axis of the valve. The number of unique flow rates (F) is related to the number of solenoids (N) as F=2N. The relationship between the size (S) of the individual gas control orifices for each of the solenoids is related to N by the relationship S=2n−1 for each individual gas control orifice (n) numbered 1 to N.