The Modern Presidential Flag, 1945-present
In 1945, shortly before his death, President Franklin D. Roosevelt asked the War and Navy Departments whether his flag, showing four stars, was still appropriate following the creation of five-star generals and admirals.  Although it was determined that the four stars on civil officials' flags were merely decorative and not an expression of relative military rank--and, in fact, that civil officials do not even have military rank--the revision of the flag went ahead anyway. 

October 25, 1945, President Truman issues Executive Order 9646 making changes to both the flag as well as the Presidential seal and coat of arms.  The most significant changes were:  (1) the substitution of a circle of white stars equal to the number of states surrounding the coat of arms, in lieu of the four stars in the corner; (2) the eagle facing his right, toward the hoist and the talon with the olive branches; (3) showing the coat of arms in the flag in full color instead of primarily in white; and (4) lightening the shade of blue in the chief of the shield. 

This new flag was first hoisted on October 27, 1945, aboard the aircraft carrier USS Franklin D. Roosevelt when President Truman went aboard to witness a fleet review in New York City.  Because the order provided that the dimensions be in accordance with military and naval custom, the President's color for ceremonial use ashore has been 52 inches by 66 inches, in conformance with Army custom, while the flag flown aboard ship, like other personal flags used by the Navy, has the proportions of approximately 7:10, the same as the U.S. union jack. 

In practice, the President's flag at sea is now in the single size of 3.60 by 5.13 feet.  Except for the increase in the number of stars from 48 to 49 in 1959 and to 50 in 1960, the Truman design is still in use today, currently as defined by Executive Order 10860 of February 5, 1960.  The fifty-star version is illustrated above.