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In base five, since there will be at most 4 of any one kind of piece, only 5 digits, 0, 1, 2, 3, and 4, are needed to represent a counting number. Base two requires only 2 digits, 0 and 1, to represent a number, but the representation of a number becomes quite lengthy: in base two, a strip contains only 2 tile, a mat contains 4 tile, a strip-mat 8 tile, a mat-mat 16 tile, a strip-mat-mat 32 tile, and a mat-mat-mat 64 tile, thus it takes a mat-mat-mat of 64 tile plus a strip-mat-mat of 32 tile plus a mat of 4 tile to total 100 tiles. So, 10010 = 11001002

Since a numeral in base two is a sequence of 0's and1's, it can be thought of as a sequence of electricalswitches where, say, an "on" switch represents a 1 andan "off" switch represents a 0. Consequently, base two,and bases which are powers of two, lend themselvesto electronic computation. For example, machine-language programming is done in base sixteen. Thisnecessitates having 16, rather than 10, digits. Forexample, when grouped by sixteens, a collection oftwo hundred tile forms 12 strips of 16 tile each with 8units left over, so in writing the base 16 numeral fortwo hundred one needs a symbol that represents 12to record the number of strips. In machine languageprogramming A, B, C, D, E, and F are used torepresent ten, eleven, twelve, thirteen, fourteen, andfifteen, respectively. With this convention, 20010 =C816. Also, for example, in base sixteen, CAD standsfor collection of 12 mats,10 strips, and 13 units. Sincein base sixteen, a mat contains 162 tile and a stripcontains 16 tile, CAD16 = 12 x 16

2 + 10 x 16 + 13 =324510. Similarly, 4F16 = 4 x 16 + 15 = 7910.

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