# How to perform logical inclusive OR operation on hexadecimal numbers?

In logic there is so called OR operation that is quite clear to me as long as it is in the binary system. For example, if I want to OR such binary values as "101" (which corresponds to decimal "5") and "110" (which corresponds to decimal "6"), you would do it this way:

101

+

110

=

111

The logic here is quite clear: if there is at least one "1", then the result must also be "1".

However, I have no idea how this operation can be performed on hexadecimal numbers. For example, if I needed to OR such hexadecimal values as "1A" (which corresponds to decimal "26") and "1F" (which corresponds to decimal "31"), how would i do that than?

1A

+

1F

=

??

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To expand on copper.hat’s answer just a little, observe that every hexadecimal digit corresponds to a string of four bits:

$$\begin{array}{c|c} \text{Hex}&\text{Bin}\\ \hline 0&0000\\ 1&0001\\ 2&0010\\ 3&0011\\ 4&0100\\ 5&0101\\ 6&0110\\ 7&0111\\ 8&1000\\ 9&1001\\ A&1010\\ B&1011\\ C&1100\\ D&1101\\ E&1110\\ F&1111 \end{array}$$

Thus, any hexadecimal number converts very easily to binary: just convert the individual digits. Hex $B94A$, for instance converts to $1011\;1001\;0100\; 1010$. (That conversion is practically hard-wired, since I earned my spending money in college writing IBM 360 assembler language programs!)

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Engineers used to (and still do) use some particular bit patterns because they are easily recognizable in hex. For example, AAAA, 5555, DEADBEEF,... – copper.hat Aug 31 '12 at 6:19
For quick reference, you can even make a 16-by-16 table of the results, all in hexadecimals. Well, maybe that's not quicker :P BTW, I like copper.hat's DEADBEEF! – Tunococ Aug 31 '12 at 6:27

Treat the hex number as binary. $1A_{16} = 11010_2$, $1F_{16} = 11111_2$, so the 'or' is clearly $1F_{16}$.

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