how would 123 base 4 look in base 5 and why?
To convert a number from one base to another, you need to first understand the positional notation system. In base 4, the digits can range from 0 to 3, and each digit's position represents a power of 4. Similarly, in base 5, the digits can range from 0 to 4, and each digit's position represents a power of 5.
To convert 123 from base 4 to base 5, we can follow these steps:
Step 1: Determine the value of the number in base 10
To convert from base 4 to base 10, we multiply each digit by the corresponding power of 4 and sum them up. In this case, we have:
1 * 4^2 + 2 * 4^1 + 3 * 4^0 = 16 + 8 + 3 = 27 (in base 10)
Step 2: Convert the base 10 number to base 5
To convert from base 10 to base 5, we need to find the largest power of 5 that is less than or equal to the number. In this case, it is 5^1 = 5.
Dividing 27 by 5, we get 5 remainder 2. The quotient represents the coefficient of the 5^1 term, and the remainder becomes the coefficient of the 5^0 term. Thus, the number 27 in base 10 can be represented as 52 in base 5.
Therefore, the number 123 in base 4 is equivalent to 52 in base 5.