Question

If 321 base 4 is divided by 23 base 4 and leaves a remainder 'R' what is the value of 'R' ?

Answer 1

R=2

23*11 base 4 is

023
230
-----
313
+ 2
------
321

Answer 2

or:


321<sub>base 4</b> = 3(4^2) + 2(4) + 1
= 48 + 8 + 1 = 57 in base 10

23<sub>base 4</b> = 2(4) + 3 = 11 in base 10

57/11 = 5 2/11
so the remainder in base 10 is 2
and since 2<sub>base 4</b> = 2<sub>base 10</b>

R = 2


Steve's method is more direct, however you have to know how to do arithmetic in base 4.

Answer 3

or:


321_{base 4} = 3(4^2) + 2(4) + 1
= 48 + 8 + 1 = 57 in base 10

23_{base 4} = 2(4) + 3 = 11 in base 10

57/11 = 5 2/11
so the remainder in base 10 is 2
and since 2_{base 4} = 2_{base 4}

R = 2


Steve's method is more direct, however you have to know how to do arithmetic in base 4.