Final answer:
To convert (8D.E)16 to other number systems: in binary, it is 1000 1101.1110; in octal, it is 415.74; and in decimal, it is 141.875.
Step-by-step explanation:
Converting the hexadecimal number (8D.E)16 to binary, octal, and decimal involves several steps. First, let's convert it to binary. Each hex digit corresponds to four binary digits, also known as bits. The hex digit '8' is '1000' in binary, and 'D' is '1101'. Since we have a hexadecimal fraction, the '.E' also needs to be converted; 'E' is '1110' in binary. So, (8D.E)16 in binary is: 8D.E = 1000 1101.1110
To convert the same number to octal, we can first convert it to binary, as we did above, and then group the binary digits into groups of three since each octal digit corresponds to three binary digits. From the binary number 1000 1101.1110, we group as follows (adding leading zeros if necessary): 010 001 101 . 111 100,which converts to the octal number 415.74.
Finally, to convert to decimal, you multiply each digit by 16 raised to the power of its position, counting from right to left starting with 0 for the digit to the right of the point. For the integer part: 8 * (16^1) + 13 * (16^0),and for the fraction part: 14 * (16^-1). This gives us: 8 * 16 + 13 + 14 * 0.0625 = 128 + 13 + 0.875 = 141.875.