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