Hexadecimal To Binary

What Does Hexadecimal To Binary Mean?

Hexadecimal to binary (X2B) is a conversion process involving the two aforementioned number systems. The original number is in hexadecimal format, base 16, and it is converted to binary format, base 2.

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The conversion can be done by converting each hexadecimal digit to its binary counterpart by adding the binary place values. In other words, it is about finding the correct combination from binary place values of 8, 4, 2, 1 that equals the decimal representation of the hex value. For example the hex value A or 10 in decimal is 1010.

Techopedia Explains Hexadecimal To Binary

Hexadecimal is often used to shorten binary values since each hexadecimal value is equivalent to four binary values or bits. There are 16 values in hexadecimal: 0 to 9 and A to F, or 0 to 15 in decimal, while there are only two values for binary: 1 and 0. Binary is often arranged in groups of 4 bits, which totals 15 when the place values of 8, 4, 2 and 1 are added.

To convert a hexadecimal value to binary, each digit is converted to 4-bit binary and then all conversions are simply concatenated. In a 4-bit binary code, all the place values are added with a 1 on it, or multiplied by 8421 with its aligned value. So the binary code 1010 is equal to 8 + 0 + 2 + 0 which is the decimal "10" or hexadecimal "A".

For example we convert the hexadecimal value "FACE" to binary:

    F (15) = 8 + 4 + 2 + 1 = 1 1 1 1
    A (10) = 8 + 0 + 2 + 0 = 1 0 1 0
    C (12) = 8 + 4 + 0 + 0 = 1 1 0 0
    E (14) = 8 + 4 + 2 + 0 = 1 1 1 0
    Concatenating: 1111 (F) 1010 (A) 1100 (C) 1110 (E)
    FACE = 1111 1010 1100 1110

Hexadecimal is significantly shorter than binary, so binary values which are the actual language used by computers are often presented to the user as hexadecimal values.

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Margaret Rouse
Technology Expert

Margaret is an award-winning technical writer and teacher known for her ability to explain complex technical subjects to a non-technical business audience. Over the past twenty years, her IT definitions have been published by Que in an encyclopedia of technology terms and cited in articles by the New York Times, Time Magazine, USA Today, ZDNet, PC Magazine, and Discovery Magazine. She joined Techopedia in 2011. Margaret's idea of a fun day is helping IT and business professionals learn to speak each other’s highly specialized languages.