Let's take a look, for example, at South Carolina
From the 1790 Census (
http://en.wikipedia.org/wiki/1790_United_States_Census)
Free White People: 140,178 (56%)
All Other Free Persons: 1,801 (<1%)
Slaves: 107,094 (43%)
From the 1850 Census (
http://www.census.gov/prod/www/abs/decennial/1850.html)
White Population: 274,563 (41%)
Free Colored Population: 8,960 (1%)
Free Blacks: 4,558 (<1%)
Free Mulattoes: 4,372 (<1%)
Slave Blacks: 372,482 (56%)
Slave Mulattoes: 12,502 (2%)
From the 1860 Census (
http://www.civilwarhome.com/population1860.htm)
Free Population: 301,302 (43%)
Slave Population: 402,406 (57%)
From the 1890 Census (
http://www.census.gov/prod/www/abs/decennial/1890.html)
Whites 462,008 (40%)
Negroes 621,781 (54%)
Mulattoes 53,400 (5%)
Quadroons 8,120 (<1%)
Octoroons 5,633 (<1%)
Chinese 34
Civilized Indians 173
From the 2010 Census (
http://quickfacts.census.gov/qfd/states/45000.html)
Population, 4,625,364
White persons, 66.2%
Black persons, 27.9%
American Indian and Alaska Native persons, 0.4%
Asian persons, 1.3%
Native Hawaiian and Other Pacific Islander, 0.1%
Persons reporting two or more races, 1.7%
Persons of Hispanic or Latino origin, 16.3%
White persons not Hispanic, 64.1%
So, some time between 1890 to present, South Carolina went from being majority Black to majority White, and the percentage of people who reported as racially mixed also fell.
I'm guessing that a lot of people with at least some African ancestry melted into the "White" population, and that most of the people in the "White" population have at least some African ancestry.