S4-4.2 Combinational Design

Work through these

• Binary adders and subtractors

  Adders and subtractors are the arithmetic core of every processor, built from the same one-bit cell repeated. Understanding how carry propagates is what later explains why fast adders are designed the way they are.

• Code converters: binary-Gray, Gray-binary, BCD-excess-3, BCD-seven-segment

  Code converters translate between representations that each exist for a reason: Gray code changes one bit at a time so a sensor never reads a spurious value, and seven-segment drives a display. The conversions themselves are routine combinational design.

• Decoders, encoders and priority encoders

  A decoder turns a binary number into one active output line, an encoder does the reverse, and a priority encoder decides what to do when several inputs assert at once. That arbitration idea returns in interrupts and bus design.

• Multiplexers, demultiplexers, comparators

  A multiplexer selects one of many inputs, a demultiplexer routes one input to many outputs, and a comparator reports which of two numbers is larger. These are the plumbing of every datapath you will meet.

• Implementing arbitrary logic functions with decoders and muxes

  Any Boolean function at all can be built from a decoder or a multiplexer with no extra minimisation. It is the unit's best trick because it shows structure and logic are interchangeable currencies.

• Lab: design and simulate a 4-bit adder-subtractor

  Design and simulate a four-bit adder-subtractor, which combines the arithmetic cell with the complement trick from the first unit. Getting the overflow behaviour right is the part that repays care.