+118608 Compute . Express your answer in base 3.
\(121_3+2122_3-1200_3-2111_3\\ =(121_3+2122_3)+(1200_3-2111_3)\)
Just doe it the same as any primary school addition and subtraction. Except it is base 3 not base 10 so you carry lots of 3 not lots of 10.
I have put each digit in a column. The 'carry' and the 'not' were added as I did the calculations.
| add base 3 |
| 1 | 2 | 1 | |
| carry1 | 2carry1 | 1carry1 | 2carry1 | 2 | |
| \(121_3+2122_3=\) | 1 | 0 | 0 | 2 | 0 |
121_3+2122_3-1200_3-2111_3
| add base 3 | 1 | 2 | 0 | 0 | |
| carry1 | 2carry1 | 1 | 1 | 1 | |
| \(1200_3+2111_3\)= | 1 | 1 | 0 | 1 | 1 |
The first one is bigger than the second one s the answer will be negative
Get the absolute value by subtracting the second from the first
| subtract base 3 | 1 | 1 no 0 | 0 no2 | 1 no 4 | 1 |
| 1 | 0 | 0 | 2 | 0 | |
| \(11011_3-10020_3=\) | 0 | 0 | 2 | 2 | 1 |
so
\(10020_3-11011_3=-(11011_3-10020_3)=-221_3\)
