Part 4/8:
Using Counting Methods to Verify Conversion
Counting the sequence of numbers in different bases helps verify the conversion. For example, counting in binary:
- 1, 10, 11, 100, 101, 110, 111 (which is 7 in decimal).
In base 4, counting up to '111' (base 4):
- 1, 2, 3, 10, 11, 12, 13, 20, 21,..., 111 (all represent preceding decimal values). The total count confirms that '111' in base 4 equals 21 in decimal.
Converting From Larger to Smaller Bases
Conversion from a larger base to a smaller one (or vice versa) requires caution due to the absence of certain digits in the smaller's set.
Example: Convert decimal 10 to base 4
Step 1: Divide 10 by 4: (10 / 4 = 2.5). The quotient is 2, and the remainder is 2.
Step 2: Record the quotient (2) and remainder (2).