In one line: Digital systems represent everything as ones and zeros, combine them with logic gates, and remember state with flip-flops clocked in step. Counters and processors are all built from these few pieces.
Core idea
A digital signal has two meaningful levels, 1 and 0. Restricting signals to two levels makes circuits robust to noise, and lets designs be reasoned about with Boolean algebra.
Gates are built from transistor switches. In CMOS, a network of p-channel transistors pulls the output up to 1, and a complementary network of n-channel transistors pulls it down to 0. Exactly one of the two networks conducts at any time.
How it works
Gates: AND, OR, NOT, NAND, NOR and XOR. NAND and NOR are each universal: any logic function can be built from just one of them.
Combinational logic. Outputs depend only on the current inputs.
- Design it from a truth table, then simplify with Boolean algebra or Karnaugh maps.
- Example: a half adder adds two bits. The sum is A XOR B, and the carry is A AND B.
- Other examples are full adders, multiplexers, and the decoder that turns a binary number into the segments of a seven-segment display.
Sequential logic. Outputs depend on inputs and stored state.
- Latches and flip-flops store a bit.
- A register is a group of flip-flops updated together on a clock edge.
- A counter is a register plus an adder, feeding its own output back each clock cycle.
The course’s design exercise is a 3-bit counter with enable, reset, load and up-or-down inputs, assembled from a register and an adder-subtractor block. It shows that design at this level means setting priorities between inputs and composing standard blocks, not drawing individual gates.
Processors are large sequential machines that loop through fetch, decode, execute. A pipelined processor overlaps the stages of successive instructions, like an assembly line, to finish more instructions per unit time. Modern instruction sets such as RISC-V keep the instructions simple so they can be pipelined efficiently.
In practice
Most digital design today is written in hardware description languages and synthesized by tools, so it looks much like software (see Software in Engineered Products). The same disciplines apply: clear interfaces, modular blocks and thorough testing. The key questions for a leader are about timing, meaning whether every signal settles before the next clock edge, and about verification, meaning how the design was tested before it was committed to silicon.
Questions to ask the experts
- What clock rate are we targeting, and what is the timing margin?
- Which blocks are standard, reused parts and which are new?
- How was the design verified before fabrication or release?
Connections
- The discipline: Electrical and Computer Engineering. What gates are made of: Semiconductor Devices.
- Where logic runs code: Embedded Microcontrollers. Hardware as code: Software in Engineered Products.
- Blocks and interfaces at the system level: Functional Flow Block Diagram.
- Capabilities exercised: Inquiry, Resourcefulness, Decision Making.
Sources
- Course lecture on the fundamentals of digital electronics; no public source.