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I am self taught in CS and came across this while looking at binary search applied to multiplication. I don't understand this part: OK, we have some x that has binary representation $10110010(1*2 + 1*2^4 + 1*2^5 + 1^7$) ...I understand this, but don't know what following means $x = 2^4(1011) + 0010$. What is name of second notation, where can I find more about this?

Thanks!

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  • $\begingroup$ Probably a bit more context is needed. The $2^4$ is not the same as the 1011 in the parenthesis in any common number system. Maybe here it is just multiplication. $\endgroup$ – Peter Leupold Oct 20 '17 at 10:06
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They've split an 8-bit byte into two four-bit nibbles (sometimes spelled "nybble"). The brackets denote multiplication; it's just saying that $$10110010 = 10000\times 1011 + 0010\,,$$ (written all in binary to avoid having two different bases in the same expression). This is just like saying, in decimal, that $$837\,487 = 1000\times837+487\,.$$ There isn't really anything to find out.

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Maybe you understand it better if it's written as

$$x=(2_{10})^4*(1011_2)+0010_2.$$

I use the index to indicate which base I use.

It's similar to saying

$$1234567 = 10^4*(123)+4567$$

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