SCALES OF NOTATION 63

126. We can change from the sexidenal to the binary scale
in two steps by applying the above two rules.
Thus 902 (D) = 21,23,31(4) = 10,01,10,11,11,01(2)

127. We can also change directly from the sexidenal to the
binary scale by a similar rule, using periods of four figures,
this because [0 is the fourth power of 2.

For applying this rule we need the digits of the sexidenal
scale exprest in the binary scale, as follows:

0= 0 4 = 100 8 = 1000 T = 1100
1= 1 5 =101 9 = 1001 2 = 1101
2=10 6 =110 ‘f = 1010 ¥ = 1110
3 =11 7 =111 0 = 1011 ¢ = 1111

Applying this rule we get 902 (l0) = 1001,1011,1101(2),
which agrees with the result obtaind above.
As another example, 5934(10) = 101,1001,0011,0100(2).

128. These rules are evidently reversible. If a number is
given in either the binary or the quaternary scale and we wish
to change to the quaternary or the sexidenal scale respectivly, we
separate the figures of the number into periods of two figures each
starting at the units figure, except that the last period may have
only one figure, and substitute for the periods the corresponding
digits. To change from the binary to the sexidenal scale we
separate into periods of four figures each starting at the umits
figure, except that the last period may have less than four figures,
and substitute for the periods the corresponding digits.

We can, then, change from any one of the bases 2, 4, 10
to either of the others directly by a simple rule.

129. We can also change similarly from the octimal notation
to the binary, and reversely, using periods of three figures.
For instance, 763(8) = 111,110,011(2).