Suppose in a system numbers are written using the digits 0, 1, and 2 with 0 <…
2024
Suppose in a system numbers are written using the digits 0, 1, and 2 with 0 < 1 < 2. What will be the binary equivalent of 222 in this system ?
- A.
11011
- B.
11010
- C.
11000
- D.
10110
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Correct answer: B
Base 3 to decimal calculation:
(222)3 = (2 × 32) + (2 × 31) + (2 × 30) = (26)10
Decimal to base 2 calculation:
Divide by the base to get the digits from the remainders:
Division | Quotient | Remainder (Digit) | Digit |
|---|---|---|---|
26/2 | 13 | 0 | 0 |
13/2 | 6 | 1 | 1 |
6/2 | 3 | 0 | 2 |
3/2 | 1 | 1 | 3 |
1/2 | 0 | 1 | 4 |
= (11010)2