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Counting
When counting in senary, we would make groups of sen (six) instead of ten. Thus, we see that there are twosen-three (236) circles below.
Adding
Multi-digit addition
In the problem below, note that 5+4 in senary is equal to 136. Thus, a 1 is carried to the next column, making the total 5 in the second column. The other problem is left for you to try.
Subtraction
In the problem below, note that we must regroup from the second column in order to have enough to subtract for the first column. When we borrow in senary, we are actually borrowing sen (six). Thus, the first column ends up with sentri (136), equivalent to 9 in decimal, so that after subtracting 5 we are left with 4. The other problem is left for you to try.
Multiplication
It is interesting to note the patterns and similarities to a decimal multiplication table:
- Multiples of 2 count up by twos, ending in 0, 2, or 4.
- Multiples of 3 end in 0 or 3.
- Multiples of 4 end in 4, 2, or 0.
- The digits of multiples of 5 add up to 5 (similar to 9 in decimal), and the last digit is decreased by one (again, similar to 9)
- Multiples of 106 act just like multiples of 10 in decimal. Even 106 squared is equal to 1006.
Fractions
Using long division, we can determine the digital form of fractions in senary. The table below lists several equivalent fractions in both senary and decimal. Digits in parentheses are repeating digits.
Note that in the first twelve (sentoo) fractions, senary has only four fractions with repeating digits, whereas decimal has six. This is because the prime factors of six (i.e. 2 and 3) are closer together than the factors of ten (i.e. 2 and 5).
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