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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

Sections Covered.

Section 1.3, Section 1.4