simplify 213 in base 4 multiply by 23 in base 4?
213 in base 4 ---> 2(4^2) + 1(4) + 3 = 39 base 10
23 in base 4 ----> 2(4) + 3 = 11
then 11*39 = 429
429 = 6(64) + 2(16) + 3(4) + 1
= 6(4^3) + 2(4^2) + 3(4) + 1
= 6231 in base 4
Unless you create yourself an addition table
and a multiplication table in base 4, the above method
is probably your best bet.
If you have the tables, you can do the calculation using
our standard algorithm for multiplication
oops, of course there is no 6 in base 4, my bad
so 429 in base 4
= 1(256) + 2(64) + 2(16) + 3(4) + 1
= 12231 in base 4
To simplify the expression, we need to convert both numbers to base 10, perform the multiplication, and then convert the result back to base 4.
First, let's convert 213 in base 4 to base 10:
2 * 4^2 + 1 * 4^1 + 3 * 4^0 = 2 * 16 + 1 * 4 + 3 * 1 = 32 + 4 + 3 = 39
Next, let's convert 23 in base 4 to base 10:
2 * 4^1 + 3 * 4^0 = 2 * 4 + 3 * 1 = 8 + 3 = 11
Now, let's multiply 39 by 11 in base 10:
39 * 11 = 429
Finally, let's convert 429 in base 10 to base 4:
429 = 2 * 4^3 + 2 * 4^2 + 0 * 4^1 + 1 * 4^0 = 2 * 64 + 2 * 16 + 0 * 4 + 1 * 1 = 128 + 32 + 1 = 161
So, the result of simplifying 213 in base 4 multiplied by 23 in base 4 is 161 in base 4.
To simplify multiplication in base 4, we need to perform the multiplication as we would in base 10, and then convert the result back to base 4.
Converting the numbers to base 10:
213 in base 4 = (2 * 4^2) + (1 * 4^1) + (3 * 4^0) = 2 * 16 + 1 * 4 + 3 * 1 = 32 + 4 + 3 = 39
23 in base 4 = (2 * 4^1) + (3 * 4^0) = 2 * 4 + 3 * 1 = 8 + 3 = 11
Multiplying the converted numbers in base 10:
39 * 11 = 429
Converting the result back to base 4:
429 in base 4 = (1 * 4^3) + (0 * 4^2) + (2 * 4^1) + (1 * 4^0) = 1 * 64 + 0 * 16 + 2 * 4 + 1 * 1 = 64 + 0 + 8 + 1 = 73
Thus, the simplified expression is 73 in base 4.