math

[Guest]

what is321 base 4 + 123 base 4 equal?

 

[daon]

what is321 base 4 + 123 base 4 equal?

321+123 = 1110

 

[soroban]

Hello, Guest!

Here it is in baby-steps . . .

What does $\displaystyle 321_4\,+\,123_4$ equal?

$\displaystyle \;\;\;a\;b\;c$
$\displaystyle \;\;\;3\;2\;1$
$\displaystyle \;\;\;1\;2\;3$
$\displaystyle \;\;----$

In column $\displaystyle c$, we have: $\displaystyle \,1\,+\,3\;=\;10\;\;('4')$
We "put down the 0, carry the 1".
$\displaystyle \;\;\;a\;b\;c$
$\displaystyle \;\;\;3\;2^{^1}\,1$
$\displaystyle \;\;\;1\;2\;3$
$\displaystyle \;\;----$
$\displaystyle \;\;\;\;\;\;\;0$

In column $\displaystyle b$, we have: $\displaystyle \,2\,+\,2\,+\,1\:=\:11\;\;('5')$
"Put down the 1, carry the 1".

$\displaystyle \;\;\;a\;b\;c$
$\displaystyle \;\;\;3^{^1}\,2\;1$
$\displaystyle \;\;\;1\;2\;3$
$\displaystyle \;\;----$
$\displaystyle \;\;\;\;\;1\;0$

In column $\displaystyle a$, we have: $\displaystyle \,3\,+\,1\,+\,1\:=\:11\;\;('5')$
Write down the entire $\displaystyle 11$.

$\displaystyle \;\;\;a\;b\;c$
$\displaystyle \;\;\;3\;2\;1$
$\displaystyle \;\;\;1\;2\;3$
$\displaystyle \;\;----$
$\displaystyle \;1\;1\;1\;0$


Therefore: $\displaystyle \,321_4\,+\,m123_4\:=\:1110_4$


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If you're desperate, change the problem to base-10,
$\displaystyle \;\;$do the addition, then change back to base-4.

$\displaystyle \;\;\;321_4\;=\;57$
$\displaystyle \;\;\;123_4\;=\;27$
. . . . . . . . . .$\displaystyle \,--$
. . . . . . . . . . .$\displaystyle 84\;=\;1110_4$