R SRR

i

62 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

Other examples in change of radix:

365(°P) = 101101101(2)
= 11231(4)
= 555(8)
= 16110)
1398('f) = 21043(5)
3312(4) = 246(F)
3312(10) = 13074(*)
212013(4) = 2439(f) = 987(0)

124. For changing from the sexidenal scale to the quater-

nary we can derive a simple rule.
In the first place the digits and radix of the sexidenal scale

are represented as follows in the quaternary scale:

 

0=0 4 =10 8 =20 © =30 0 = 100
1=1 S5=11 9 =21 e =31
2 =2 Boa 12 P =22 ¥ = 32
3=3 =13 0 =23 ¢ =33
Consider the number 90 2 (0), which equals
DX U X D42,
9 X 102 = 21 X 1002(4) = 21,00,00 (4)
O X110 =23X100(4) = 23,00 (4)
2 = 31 (4)

Hence 902 (I0) = 21,23,31 (4)

The rule evidently is to substitute for the digits of the number
written in the sexidenal scale their representations in the quater-
nary scale, each occupying a period of two figures.

The period of two figures is due to the fact that [0 is the

second power of 4.
As another example, 3924(10) = 3, 21 02,10(4).

125. We can in just the same way change from the quater-
nary scale to the binary, because 4 is the second power of 2.
For this change 2 is replaced by 10 and 3 by 11.
For example, 231(4) = 10,11,01(2)
21,23,31(4) = 10,01,10,11,11,01(2)