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What is the hexadecimal representation of the binary number 11110000?

The hexadecimal representation of the binary number 1111000011110000 is F0F0.

To convert a binary number to hexadecimal, we start by grouping the binary digits into sets of four, beginning from the right. In this instance, the binary number 1111000011110000 is already organized into a group of four. Each group of four binary digits corresponds to a single hexadecimal digit.

Specifically, the binary number 11111111 corresponds to the hexadecimal digit FF, while the binary number 00000000 corresponds to the hexadecimal digit 00. Consequently, the hexadecimal representation of the binary number 1111000011110000 is F0F0.

This conversion relies on the fact that both binary and hexadecimal are positional numeral systems. Hexadecimal is a base-16 system, whereas binary is a base-2 system. Each hexadecimal digit represents four binary digits, which is why we group the binary digits in sets of four. This grouping makes hexadecimal a convenient format for representing binary data, as it significantly reduces the number of digits required.

It is important to note that the hexadecimal system employs the digits 090-9 and the letters AFA-F to represent values from 00 to 1515. In our example, the binary group 11111111 is equivalent to 1515 in decimal, represented as FF in hexadecimal. Meanwhile, the binary group 00000000 equals 00 in decimal, which is represented as 00 in hexadecimal. Therefore, the binary number 1111000011110000 is represented as F0F0 in hexadecimal.

Answered by: Dr. Isabella Harris
A-Level Computer Science Tutor
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