Worked Example 1
Convert 45 from base ten into base two.
Divide repeatedly by 245, 22, 11, 5, 2, 1, 0 with remainders 1, 0, 1, 1, 0, 1.
Read upwards45 = 101101 in base two.
Check by converting back32 + 8 + 4 + 1 = 45. It agrees.
Worked Example 2
Convert 73 into base five, and 243 from base five back into base ten.
73 into base fiveRemainders 3, 4, 2, read upwards: 243 in base five.
243 back into base ten2 × 25 + 4 × 5 + 3 × 1 = 73. The two conversions agree.
Notice the digits usedIf your base five answer contains a 5 or a 6, you have made a mistake: those digits do not exist in that base.
1 more worked examples - sign in to see them all.