Find x and y.

Question

Find x and y.

Quizplus · Accepted Answer

There are several conventions for converting hexadecimal to decimal or binary, but one common method is to treat each digit as a separate hexadecimal number, convert it to a four-bit binary number, and concatenate the results. For example, the first group of digits 11eb11e8 corresponds to the binary string 00010001111010110001000111101000. We can partition this string into two parts of 16 bits each, which gives us the binary representations of x and y:

x: 0001000111101011 = 1179
y: 0001000111101000 = 1176

To see why this works, note that the first digit of the hexadecimal representation corresponds to the 16^7 place in the binary representation, the second digit corresponds to the 16^6 place, and so on, up to the last digit, which corresponds to the 16^0 place. Therefore, by converting each digit to a four-bit binary number, we can determine its contribution to the overall value. Since there are 8 digits in the hexadecimal string, we can partition it into two 4-digit strings, each of which corresponds to a 16-bit binary number. Finally, we convert each binary number to its decimal equivalent to obtain the values of x and y.

Find X and Y