Question

Arithmetic in Other Bases

Discuss whether (and how) the four basic arithmetic algorithms with which you’re familiar extend to other bases. Then try to work out the problems below, WITHOUT converting to base ten and back. Work directly in the given bases.

1. (a) base six (b) binary (base two) (c) hexadecimal (base sixteen)

4 0 4 3 1 1 0 0 1 1 3 A E

+ 313       + 1 1 1 0 1 + B 0 5

--------------- ------------------ ------------------

2. (a) base eight (b) binary (base two) (c) base eleven

2 6 1 3 1 1 0 0 1 1 2 3 A 5

- 7 0 4 - 1 1 1 0 1   - 6 0 6

--------------- -------------------- ---------------

3. (a) ternary (base three) (b) base nine

2 0 2 1 8 8

x 1 2 x 4 6

-------------- -------------

4. LONG DIVISION: (a) heximal (base six)   (b) binary (base two)

13)5430 110)101101

Note: In bases larger than ten, the characters A, B, C, D, E, F represent the numbers ten through fifteen.

Answer 1