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I have seen it as 1:64 and 3/16. I think the 1:64 means 1 foot = 64 feet, and 3/16th of an inch = 1 foot.
 

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They are both correct. 1/64th is the accurate value used to scale down a prototype dimension to S scale. Everything in S scale is 1/64 full size. The O scale equivalent of this number is 1/48.
3/16" is the resulting size in S scale of a prototype one foot. The O scale equivalent of this value is 1/4". Recognize that the 3/16" value has a very slight rounding error to simplify the fraction.
 

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Also, 1/64inch equals 1 inch for the prototype. 12/64 inch equals 3/16 inch equals 1 prototype foot
 
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