Binary and hexadecimal are both number systems used in computing and digital systems.

Binary is a base-2 system, which means it uses only two digits – 0 and 1 – to represent all numbers. In binary, each digit represents a power of 2, with the rightmost digit representing 2^0 (1), the next representing 2^1 (2), the next representing 2^2 (4), and so on. For example, the binary number 1011 represents the decimal number 11, because 1×2^3 + 0x2^2 + 1×2^1 + 1×2^0 = 8 + 0 + 2 + 1 = 11.

Hexadecimal is a base-16 system, which means it uses 16 digits – 0 to 9 and A to F – to represent all numbers. In hexadecimal, each digit represents a power of 16, with the rightmost digit representing 16^0 (1), the next representing 16^1 (16), the next representing 16^2 (256), and so on. For example, the hexadecimal number AB represents the decimal number 171, because 10×16^1 + 11×16^0 = 160 + 11 = 171.

Converting between binary and hexadecimal is useful in computing because it allows for more efficient representation of large numbers. One hexadecimal digit can represent four binary digits, so converting a binary number to hexadecimal can make it more compact and easier to work with. To convert a binary number to hexadecimal, you can group the binary digits into sets of four, starting from the rightmost digit, and then convert each set to its hexadecimal equivalent. For example, the binary number 11011010 can be grouped as 1101 1010, which can be converted to the hexadecimal number DA.

To convert a hexadecimal number to binary, you can simply convert each hexadecimal digit to its four-digit binary equivalent. For example, the hexadecimal number 4F can be converted to the binary number 01001111.