Jan 22, 2019

#2**+2 **

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

\(10020_3-11011_3=-(11011_3-10020_3)=-221_3\)

.MelodyJan 22, 2019