A2 - circuit models

composed of wires, that carry the symbols, and gates, that perform the 'precise rules' on symbols
- eg: NOT, AND, OR, XOR, NOR
- all gates have truth tables defining the precise rules
they are fixed, ie. do not change with computation
they can have different numbers of inputs and outputs
gates, and therefore circuits, can be represented as functions:

f : {0, 1}^{n} \to {0, 1}^{m}

where, $m \neq n$

if $m = 1$ , these are called boolean functions and circuits
for $n$ -bit inputs, there are $2^{2^{n}}$ boolean functions
the $0$ , $1$ input are called ancilla or work bits
universality is the notion that any circuit can be composed using a fixed set of gates

theorem 1.1

classical circuits are universal

operator	symbol
AND	$\land$
OR	$\lor$
XOR	$\oplus$
NOT	$\bar{}$

considering a NAND gate, different inputs lead to the same output
thus according to thermodynamics, the gate is irreversible

theorem 1.2 | landauer's principle

the erasure of a single bit, if performed at a temperature, $T$ , has an energy cost of $W = k_{B} T \ln 2$

this is a fundamental limit
there are larger causes of inefficiency, eg: resistance, capacitance, etc.
this led to the development of reversible classical computation, and soon after, quantum computation