and what's 123 / 2 in base 5 and 11011 / 11 in base 2? i am lost

_{}123_{5}/2_{5} = (1(5)^2 + 2(5)^1 + 3(5)^0)/2 = 19_{10}

Convert back to base 5, 19/5 = 3 mod 4. 3(5)^1 + 4(5)^0 = 30 + 4 = 34_{5}

11011_{2 } = 1(2)^4 + 1(2)^3 +0(2)^2 +1(2)^1 +1(2)^0 = 27_{10
}

11_{2 }= 3_{10 27/3 = 9}

_{ }Convert back to base 2 and 9 = 1001_{2}_{
}

## Comments

Thank you!

George, it makes no sense to write "19/5 = 3 mod 4." I take what you mean is that 5 goes into 19 three times with a remainder of 4, but that's not what the "mod" notation means. If you want to write that 19/5 is 3 remainder 4, you should just write "19/5 = 3 r4."

The "mod" notation is used as follows: if a, b, and c are

integers, then "a = b mod c" means that "a - b is divisible by c" -- or, if b is between 0 and c-1 inclusive, you can interpret this as saying "a has remainder b when divided by c."That's why "19/5 = 3 mod 4" makes no sense: first, you can use a rational number in a "mod" statement, and second, it looks like you're saying the number has remainder 3 when divided by 4.

The write way to use mod notation here would be to say "19 = 4 mod 5" (in other words 19 has remainder 4 when divided by 5). The mod notation doesn't take into account how many times c actually goes into a.

There's a typo in my comment that I can't edit to fix: it should say "

first, you CAN'T use a rational number in..."