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Compute \(121_3+2122_3-1200_3-2111_3\). Express your answer in base 3.

 Jan 22, 2019
 #1
avatar+23494 
0

-221   is waht online base 3 calc says

 Jan 22, 2019
 #2
avatar+109468 
+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

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

.
 Jan 22, 2019

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