plz solve for me too hard
show step payuto
123_(base4) = N_(base8 )
1234 = 4^2 + 2*4 + 3
= 2*8 + 8 + 3
= 338
explain plz sir steve
Steve is simply using the definition of a number with a different base.
Just like
57810 = 5(10^2) + 7(10^1) + 8(10^0)
1234 = 1(4^2) + 2(4) + 3
= 16 + 8 + 3
= 24 + 3 ---> Steve noticed the multiples of 8
= 3(8) + 3
= 338
To solve this problem, we need to convert the number 123 from base 4 to base 8. Let's break down the steps:
Step 1: Convert 123 from base 4 to base 10
To do this, we need to multiply each digit of the number by the corresponding power of 4 according to its position, and then sum them up.
The given number in base 4 is 123, which represents:
(1 * 4^2) + (2 * 4^1) + (3 * 4^0)
= (1 * 16) + (2 * 4) + (3 * 1)
= 16 + 8 + 3
= 27 in base 10.
Step 2: Convert 27 from base 10 to base 8
To convert from base 10 to base 8, we need to perform successive division by 8 and keep track of the remainders until the quotient becomes zero.
Dividing 27 by 8, we get:
27 ÷ 8 = 3 remainder 3
So, the remainder is 3 at this stage. Now, we divide the quotient (which is 3) by 8 again:
3 ÷ 8 = 0 remainder 3
Since the quotient is now zero, we stop the division process.
Step 3: Write down the remainders in reverse order
The remainders we obtained during the division process, starting from the last remainder, are 3, 3. Therefore, we write these remainders in reverse order.
So, N in base 8 is 33.
Therefore, 123 in base 4 is equivalent to 33 in base 8.