Hardware fundamentals

Bits as the binary model of digital values, buses that group bits into signals, binary place value, hexadecimal notation, and how width determines the unsigned range.

NOT, AND, OR and XOR as rules from input bits to an output bit, the truth table that states each rule completely, and how a requirement in words becomes a logic expression.

Selecting and joining bits as wiring that costs no gate, then three circuits built from gates, the multiplexer that chooses, the decoder that points and the adder that carries, and how to tell wiring from an operation.

Two's complement, why one bit pattern is two numbers depending on how it is read, what widening and narrowing do to a value, and the difference between a lost carry and an overflow.

Why a circuit needs memory, the register with its D input and Q output, and the difference between the value a register holds now and the value it will hold after the next clock edge.

The clock's period, edge and cycle; the enable that chooses between updating and holding; and reset by kind, polarity and priority, including why a clear wins over an enable.

Reading a waveform against the rising edge, telling apart driving an input, sampling it at the edge and observing the output after it, and why one or two register stages delay a value by one or two cycles.

From a requirement to a design under test and its testbench; what compile, elaborate, simulate and synthesize each do; normal, boundary and reset cases; and how to reason from a first mismatch to a likely cause.