Simplify 213 base 4 * 23 base 4?
If you need to put that 39*11 = 429 back to base 4
4^0 = 1
4^1 = 4
4^2 = 16
4^3 = 64
4^5 = 256
4^6 = 1024
well 429 / 256 = 1.6 something so
first digit is 1 with 429-256 left = 173
173/64 = 2.7..
so second digit is 2 with 173 - 128 left = 45 left
45/16 = 2.8 ....
so third digit is 2 with 45 - 32 = 13 left
13/4 = 3.25
so fourth digit is 3 with 13 - 12 = 1 left
so fifth digit is 1
12231 in base four
(2*16 + 1*4 +3)(2*4+3)
=
39*11
To simplify the expression 213 base 4 * 23 base 4, you need to multiply the two numbers in base 4 and simplify the result. Here's how you can do it:
Step 1: Convert the numbers 213 base 4 and 23 base 4 to decimal form.
To convert a number from base 4 to decimal, you need to evaluate each digit in the number multiplied by the corresponding power of 4.
For 213 base 4:
2 * 4^2 + 1 * 4^1 + 3 * 4^0 = 2 * 16 + 1 * 4 + 3 * 1 = 32 + 4 + 3 = 39
For 23 base 4:
2 * 4^1 + 3 * 4^0 = 2 * 4 + 3 * 1 = 8 + 3 = 11
So, 213 base 4 is equivalent to 39 in decimal form, and 23 base 4 is equivalent to 11 in decimal form.
Step 2: Multiply the decimal values of the two numbers.
39 * 11 = 429
So, the result of multiplying 213 base 4 and 23 base 4 is 429 in decimal form.
Therefore, the simplified expression is 429.