Skip to main content ☰ Contents Index You! < Prev ^ Up Next > \(\newcommand{\powerset}[1]{\mathcal{P}(#1)}
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Section C.3 R2: Computer Arithmetic
Synopsis.
Introduce the binary adder, make clear that it is just a combinational circuit and prove the addition of individual bits by a value table and prove that addition on bit strings it is sound with respect to the unsigned interpretation.
Make clear that the exact result needs one bit more than the operands are long and show how to use it to detect overflows.
Show how we can use modulo arithmetic to implement subtraction using addition.
Introduce signed numbers and show that addition and subtraction as we defined it is also sound on them.
Make clear that overflows have to be determined differently on signed numbers.
Explain sign and zero extension (will be of some importance later on when talking about load instructions in the machine code section.)
Bonus: Shifts
