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First draft of shift operations

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John Winans 2018-05-28 12:30:27 -05:00
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book/binary/chapter.tex
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@ -806,14 +806,53 @@ left to form a 32-bit fullword.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Shifting} \section{Shifting}
Seems like a good place to discuss logical and arithmetic shifting. We were all taught how to multiply and divide decimal numbers by ten
by moving (or {\em shifting}) the decimal point to the right or left
respectively. Doing the same in any other base has the same effect
in that it will multiply or divide the number by the value of the base.
shift left logical Multiplication and division are only two reasons for shifting. There
can be other occasions where doing so is useful.
shift right logical As implemented by a CPU, shifting applies to the value in a register
and the results stored back into a register of finite size. Therefore
a shift result will always be truncated to fit into a register.
shift right arithmetic Note that when dealing with numeric values, any truncation performed
during a right-shift will manifest itself as rounding toward zero.
\subsection{Logical Shifting}
Shifting {\em logically} to the left or right is a matter of re-aligning
the bits in a register and trncating the result.
\enote{Redraw these with arrows tracking the shifted bits and the truncated values}%
To shift left two positions:
\DrawBitBoxUnsignedPicture{10111000000000000010}\\
\DrawBitBoxUnsignedPicture{11100000000000001000}
To shift right one position:
\DrawBitBoxUnsignedPicture{10111000000000000010}\\
\DrawBitBoxUnsignedPicture{01011100000000000001}
Note that the vacated bit positions are always filled with zero.
\subsection{Arithmetic Shifting}
Some times it is desirable to retain the value of the sign bit when
shifting. The RISC-V ISA provides an arithmetic right shift
instruction for this purpose (there is no arithmetic left shift for
this ISA.)
When shifting to the right {\em arithmetically}, vacated bit positions are
filled by replicating the value of the sign bit.
An arithmetic right shift of a negative number by 4 bit positions:
\DrawBitBoxSignedPicture{10111000000000000010}\\
\DrawBitBoxSignedPicture{11111011100000000000}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@ -821,7 +860,7 @@ shift right arithmetic
\enote{Consider refactoring the memory discussion in RV32 reference chapter \enote{Consider refactoring the memory discussion in RV32 reference chapter
and placing some of it in this section.}% and placing some of it in this section.}%
When transferring data between its registers registers and main memory a When transferring data between its registers and main memory a
RISC-V system uses the little-endian byte order.\footnote{ RISC-V system uses the little-endian byte order.\footnote{
See\cite{IEN137} for some history of the big/little-endian ``controversy.''} See\cite{IEN137} for some history of the big/little-endian ``controversy.''}