Picking with a switch

One selector bit, two data lines, one output. The circuit every CPU uses a million times a second. Build a 2-to-1 multiplexer — digital's answer to a railway switch.

What you'll learn

• What a multiplexer (MUX) is and why every CPU needs thousands of them.
• How a single Select bit picks between two inputs.
• The canonical build: Output = (A ∧ ¬Select) ∨ (B ∧ Select).

The idea

A 2-to-1 MUX is a decision gate. It has:

• Input A and Input B — the two things you could choose.
• Select — the switch that decides which one to use.
• Output — whichever input Select pointed at.

The rule in English: "if Select is OFF, send A through; if Select is ON, send B through". Everything else about A or B is ignored once Select has decided.

The build

The cleanest construction uses one AND per data line, gated by Select (and its inverse), then an OR to merge:

                   ┌────┐
 Input A ──────────┤    │
                   │AND ├──┐
 Select  ──NOT─────┤    │  │
                   └────┘  │   ┌────┐
                          ├─┤ OR ├── Output
                           │  └────┘
                   ┌────┐  │
 Input B ──────────┤    │  │
                   │AND ├──┘
 Select  ──────────┤    │
                   └────┘

Three inputs, eight truth-table rows. Half of them follow A, the other half follow B — exactly what the select bit is for.

The challenge

Place three Levers labeled Input A, Input B, and Select. Use a NOT, two AND gates, and one OR to build the MUX. Send the OR's output to a Lamp labeled Output.

Where this leads

Multiplexers are how CPUs route data. When your processor picks which register to read, that's a big MUX. When the ALU selects between AND, OR, XOR, and ADD results, that's a MUX. When a memory bus reads from one of 64 cells, that's a tree of MUXes. You'll use this pattern in lesson 8 to build a tiny ALU.