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After thinking about this, I guess it is just a matter of convention.  The BDY is 2 * the semi-annual yield so when you have the annual rate of 0.0537787 and you want to go back to semi-annual, you have to think in terms of 1/2 a year so the exponent is 0.5, not 180 days.  
Let me know if my reasoning is incorrect, thanks.

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