1.) Convert (547)_10 to the _6 notation
2.) Convert (6A3)_12 to the decimal notation.
Note: _10 and _6 mean base 10 and base 6, respectively.
Hello, fifthrapiers!
There is a "trick" to converting to another base . . .
1) Convert 547 to base-6.
1. Divide the number by 6, note the remainder. .547 ÷ 6 = 91, rem. 1
2. Divide the quotient by 6, note the remainder: .91 ÷ 6 = 15, rem. 1
3. Repeat step 2 until a 0 quotient is reached:. . . 15 ÷ 6 = 2, rem. 3
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 ÷ 3 = 0, rem. 2
Now read up the remainders.
Answer: . 547 .= .2311_6
2) Convert (6A3)_12 to base-10.
(6A3)_12 .= .6·12² + 10·12 + 3·1 .= .987
When using a base higher than 10 we need symbols for numbers greater than 9 but less than 10. So the typical count goes:
1 2 3 4 5 6 7 8 9 A B C D ... 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D ... 20 etc.
For base 12 we get:
1 2 3 4 5 6 7 8 9 A B 10 11 12 13 14 15 16 17 18 19 1A 1B 20 etc.
-Dan