5.1: The Sign Extend Unit

Last updated
Save as PDF

Page ID: 27266

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

The immediate values which can be part of an instruction are 8 bits, and can be used as an input to the ALU. However, the ALU accepts inputs which are 16 bits. Therefore, immediate values which are passed to the CPU must be expanded to fill 16 bits. The question is how to fill in the high 8 bits when expanding immediate values from 8 to 16 bits.

Remember that all the immediate values passed to the CPU are integers; the top (left-most) bit of the value determines the sign. If the 2’s complement number is positive, leading 0s have no effect on the number. For example, 0101₂ = 0000 0101₂ = 5₁₀. In a negative 2’s complement number, leading 1s have no effect on the number. Thus 1011₂ = 1111 1011₂ = -5₁₀. Thus to extend an integer the left-most bit is extended into the new binary digits. This is what the sign extend unit is doing, extending the 7^th bit to positions 8-15 to translate the 8-bit integer into a 16- bit integer.

Screen Shot 2020-07-03 at 12.19.22 PM.png