Arithmetic#

Gates do math.

Addition, subtraction, comparison, and parity are just particular combinational functions — truth tables large enough that nobody writes them out by hand, built instead from repeating cells. A full adder chained N times is an N-bit adder; add a mode input and it becomes the core of an ALU. These are the blocks where propagation delay stops being abstract, because a carry has to ripple across every stage before the answer is valid.

Sections#

• Half & Full Adders — The one-bit cell that all binary arithmetic is built from.
• Subtractors — Subtraction as addition of a two’s-complement number.
• Magnitude Comparators — Deciding greater-than, less-than, or equal in hardware (distinct from the voltage comparators in Analog Helpers).
• Parity & Error Detection — Cheap integrity checks built from XOR trees.
• ALU — Where arithmetic and logic functions are selected under control — the ancestor of the CPU datapath.