The proleptic Gregorian calendar is produced by extending the Gregorian calendar backward to dates preceding its official introduction in 1582. In countries that adopted the Gregorian calendar later, dates occurring in the interim (between 1582 and the local adoption) are sometimes "Gregorianized" as well. For example, George Washington was born on February 11, 1731 (Old Style), as Great Britain and its possessions were using the Julian calendar until September 1752. After the switch, that day became February 22, which is the date commonly given as Washington's birthday.
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The Wikipedia article has much more detail, including a conversion table.