# Understanding How Double Precision Numbers are Stored in a Computer

I am reading Numerical Analysis by Walter Gautschi. I am somewhat confused by the following quote from page $$5$$:

To increase the precision, one can use two machine registers to represent a machine number. In effect, one then embeds $$\mathbb{R}(t, s) \subset \mathbb{R}(2t, s)$$, and calls $$x \in \mathbb{R}(2t, s)$$ a double-precision number.

(Here $$t$$ represents the number of allowable binary digits in the mantissa, and $$s$$ represents the number of binary digits allowable in the exponent.)

Can someone please explain what is going on here with the "machine register"? Some questions that I have are: instead of using two registers, why not just use one of bigger size? Apparently some registers have a different size, because the exponent is also stored in a register, and $$r$$ may not equal $$s$$.

Secondly, double-prevision seems to be defined in terms of a "native precision" already intrinsic to the machine. But on the other hand, I thought double precision was a fixed thing determined by IEEE.

My Background I am a math major taking my first Numerical Analysis course. I do not have any prior experience with computers (except day-to-day use of course) or numerical mathematics.