African numeration system are numerous and varied. The most common are numeration systems based on 2, 5, 10, and 20 or a combination.
Numeration based on the number two is widespread and unique to African numeration systems. It can be seen in the method of doubling. Divination systems--Ifa, Cedento, and Vodun make use of doubling. The ancient Egyptians continuously used base two for calculations. The Ishango Bones used a doubling sequence. Twins are sacred in African culture. Numbers are typically express by doubling. The Shambaa language of Tanzania express 8 as " ne na ne", four and four.
Makhwa people in Mozambique use 5 and 10 to express numbers. The Nyungwe in Mozambique use only base 10. The Balante in Guinea-Bissau use 5 and 20. The Bete people of Cote d'Ivoire uses three bases: 5, 10, and 20.The Bambara of Mali and Guinea have a 10 and 20. Base 6 exists. The Bulanda (West Africa) use 6. the Huku of Uganda uses a base 12.
Numbers are constructed by using arithmetic functions of multiplication, addition, and subtraction.
The Bulanda of West Africa (base 6) express 7 as 6 1( six one or six plus one), 8 as 6 2.
The Adele count koro (6), koroke (6 1 = 7), nye (8) and nyeki (8 1 = 9). Adding ki or one at the end.
The Huku of Uganda the number words for 13, 14, 15 are formed by the addition of 1, 2 or 3 to twelve.
The Tschwa express 60 as thlanu wa makuma ni ginwe, "five times ten plus one more (ten)".
Large numbers are constructed by using completely different words or using a base word as part of a related larger number.
The Bangongo of Zaire express kama for 100, lobombo for 1,000, njuku for 10,000, lukuli for 100,000 and losenene for 1,000,000,
The Ziba of Tanzania uses kumi (10) to express larger numbers. They express tsikumi for 100, lukumi for 1,000, and kukumi for 10,000.
Numeration Systems of major African states and empires
Gerdes, Paul and Cherinda, Marcos(1993, November). Words, gestures and symbols. Unesco Courier
MATSUSHITA, Shuji. Decimal vs Duo-Decimal, an interaction between two systems of numeration, by the Dozenal Society of Great Britain
La Fontane, Jean sybil (2004). The Interpretation of Ritual: Essays in Honour of A.I. Richards. Routledge. pp. 320.
Description of the Yoruba number system @! the Prentice Hall website
Eglash, R. African Fractals: Modem Computing and Indigenous Design (Rutgers University Press, 1999.)
Egyptian Counting. Mathematics of the African diaspora, at The Mathematics Department of The State University of New York at Buffalo, by Scott W. Williams
Graham, Nicholas. Ancient Egyptian Math Is Identical To Math Used In Modern Computers. Huffington Post 12-16-2010.
A Night Of Numbers - Ethiopian Multiplication by BBC