Digital logic — from decisions to state

Start with a question

How can a machine make a decision, add a value and remember the result for the next operation? This path answers that question at the digital-logic level. It builds from a two-valued rule to a small clocked system, with no programming environment or electronics kit required.

The articles and exercises are in English. You need basic arithmetic and the ability to read a table. Binary place values are introduced in the adder lesson. Study at your own pace; a useful pattern is to read one article, reproduce its example, then follow the next linked step.

Follow the seven steps

1. Boolean algebra: evaluate AND, OR and NOT and list every combination of inputs.
2. Logic gates: treat those rules as components; derive NAND and distinguish a truth table from an electrical specification.
3. Gate workbench: predict the outputs of AND, OR, NOT and XOR, then check them interactively or against the static tables.
4. Combinational logic: derive a selector expression and prove that it chooses the requested input.
5. Binary adders: follow a carry through four positions and explain why a result may need an extra bit.
6. Memory and registers: distinguish a stored value from its changing input; calculate the capacity and addressing of a small memory.
7. Sequential logic: combine arithmetic and storage, trace a counter and identify the time available between edges.

The linked reading steps below use the canonical articles rather than duplicate their explanations. The older logic-to-circuits path remains a shorter introduction with historical context.

Check your understanding

Before considering the path complete, solve these without looking at the answers:

• Which of OR and XOR returns 0 for inputs 11?
• With D0 = 1010 and D1 = 0111, what does a four-bit selector return for S = 1?
• What are the complete unsigned result and retained four-bit result of 1111 + 0001?
• How many payload bytes are in eight words of sixteen bits each?
• Starting at counter state 101, what happens over enable values 1, 0, 1 with reset held at 0?

Answers and scope

The distinguishing gate is XOR: its result for 11 is 0. The selector returns 0111. The unsigned sum is 10000 and the retained four-bit value is 0000. The memory holds sixteen payload bytes. The counter visits 110, 110 and 111.

You should also be able to name a limit of each model: a gate table omits electrical behavior, a combinational equation omits settling time, a register trace assumes valid timing, and a synchronous counter needs a clocking contract.

This completes the first digital-logic block, not the full planned “Build a computer from scratch” curriculum. Continue with digital control and datapaths for finite-state machines, an ALU and synchronous interfaces. Processor organization builds on those contracts; hardware construction requires additional implementation work. The source course is a reference for the subject progression; these articles, worked values and completion exercises are original.