Convert 1A3D.2 to base 10
To convert 1A3D.2 from base 16 to base 10 (decimal), we need to consider the place values of each digit.
The number 1A3D.2 can be broken down as follows:
1 * 16^3 + A * 16^2 + 3 * 16^1 + D * 16^0 + 2 * 16^(-1)
To convert the hexadecimal letters (A and D) to base 10, we substitute A with 10 and D with 13.
1 * 16^3 + 10 * 16^2 + 3 * 16^1 + 13 * 16^0 + 2 * 16^(-1)
Simplifying the equation:
1 * 4096 + 10 * 256 + 3 * 16 + 13 * 1 + 2 * 0.0625
4096 + 2560 + 48 + 13 + 0.125 = 6729.125
Therefore, 1A3D.2 in base 10 (decimal) is equal to 6729.125.
To convert a number in any base to base 10, you need to multiply each digit by the corresponding power of the base and then add them all together.
In this case, the number is in base 16, or hexadecimal. To convert 1A3D.2 to base 10, follow these steps:
1. Separate the whole part and the fractional part. In this case, we have 1A3D and 2 as the whole and fractional parts, respectively.
2. Convert the whole part to base 10 by multiplying each digit by the corresponding power of 16 and adding them together:
1A3D = (1 * 16^3) + (A * 16^2) + (3 * 16^1) + (D * 16^0)
A in base 16 is equivalent to 10 in base 10.
D in base 16 is equivalent to 13 in base 10.
Performing the calculation:
1 * 16^3 + 10 * 16^2 + 3 * 16^1 + 13 * 16^0
= 4096 + 2560 + 48 + 13
= 6717
So, 1A3D in base 16 is equivalent to 6717 in base 10.
3. Convert the fractional part to base 10 by multiplying each digit by the corresponding power of 16 and adding them together:
2 * (16^-1)
= 2 * (1/16)
= 2/16
= 0.125
So, 2 in base 16 is equivalent to 0.125 in base 10.
4. Combine the results from steps 2 and 3:
1A3D.2 in base 16 is equivalent to 6717.125 in base 10.
To convert a number from any base to base 10, we multiply each digit of the number by the corresponding power of the base and add them together.
In this case, the number is 1A3D.2, which is in base 16 (hexadecimal). To convert it to base 10, we need to multiply each digit by the corresponding power of 16.
Let's break down the number:
1A3D.2
The digit '1' is in the leftmost position, which represents the highest power of the base. In this case, 16^3. The 'A' represents the value 10 in base 10, '3' represents 3, 'D' represents 13, and '2' represents 2.
Now, let's calculate the decimal equivalent:
1 * 16^3 = 4096
A * 16^2 = 10 * 16^2 = 10 * 256 = 2560
3 * 16^1 = 3 * 16 = 48
D * 16^0 = 13 * 16^0 = 13 * 1 = 13
2 * 16^-1 = 2 * (1/16) = 2/16 = 0.125
Adding all the results together:
4096 + 2560 + 48 + 13 + 0.125 = 6727.125
Therefore, the decimal equivalent of 1A3D.2 in base 10 is 6727.125.