3.2 Decoders, Multiplexers, and ALUs

Section 3.1 combined gates into larger truth-table rules. Real processors reuse several especially useful combinations. This section develops three of them from zero:

• a decoder activates one destination;

• a multiplexer chooses one source;

• an arithmetic logic unit (ALU) computes several candidate operations and exposes the selected result.

A decoder turns a binary code into one selected line

A decoder reads an $n$-bit input code and can distinguish up to $2^n$ outputs. A 2-to-4 decoder reads address bits A1A0 and controls Y0 through Y3.

When enable input EN is 1, exactly one output is active. This is called one-hot output.

“Any” means the address does not matter while EN=0. The enable signal lets a larger system turn the entire decoder on or off.

Later, address-decoding circuits will use this idea to select memory chips and I/O devices.

Lab 1 — dispatch a request to one device

Translate a device number into two address bits, control EN, and observe the one-hot output lanes.

Check your understanding

A multiplexer chooses one input source

A multiplexer, often shortened to MUX, has several data inputs but one output. Select bits determine which input is connected logically to the output.

For a 4-to-1 MUX:

The MUX does not combine all four inputs. It routes one of them. If D2 changes while S1S0=00, Y does not change because D0 remains selected.

An ALU computes candidate operations

An arithmetic logic unit is a combinational block that performs arithmetic and bitwise logic. A simple 4-bit ALU might support:

The operation blocks can produce candidates in parallel. A MUX controlled by the select bits exposes one candidate as the ALU result.

The ALU may also produce status signals. Two useful examples are:

• carry flag (CF): addition produced a bit beyond the fixed width;

• zero flag (ZF): every result bit is 0.

Chapter 2 already showed why fixed-width addition can wrap. Later chapters will connect these flags to 8086 instructions and conditional branches.

Lab 2 — configure a miniature ALU datapath

Set 4-bit operands and selection signals. Compare all candidate operations, then route the required one while watching CF and ZF.

Check your understanding

Distinguish the three blocks

All three blocks are combinational: current inputs determine current outputs. A processor also needs hardware that keeps a value after the input changes. That requires state and feedback, which begin with latches and flip-flops.