🧩 7-tuple Definition

The standard Turing machine model is defined by the following 7-tuple:

$$M = \langle Q, \Sigma, \Gamma, \delta, q_0, B, F \rangle$$
\(Q\): Finite set of states 如 \(Q = \{q_0, q_1, q_2, \text{halt}\}\)
\(\Sigma\): Input alphabet 本实验 \(\Sigma = \{1, +, \times\}\)
\(\Gamma\): Tape alphabet \(\Gamma = \{1, +, \times, B, X, Y, \dots\}\)
\(\delta\): Transition function \(\delta: Q \times \Gamma \to Q \times \Gamma \times \{L, R\}\)
\(q_0\): Initial state 通常为 \(q_0 \in Q\)
\(B\): Blank symbol Represents empty cell on tape
\(F\): Set of final states \(F \subseteq Q\)，通常包含 \(\text{halt}\) 状态

⚙️ Transition Function

\(\delta(q, a) = (q', b, D)\)
→
Current State \(q \in Q\) Current state of the machine
●
Read Symbol \(a \in \Gamma\) Character at current head position
✎
Write Symbol \(b \in \Gamma\) Overwrite character in current cell
←/→
Move Direction \(D \in \{L, R\}\) L for left, R for right
✓
Next State \(q' \in Q\) New state after transition

"The machine determines the next action based on current state and tape symbol"

🧩 Binary Turing Machine Definition

Based on the standard 7-tuple, adapted for binary arithmetic operations:

$$M = \langle \{q_0, \dots\}, \{0, 1\}, \{0, 1, +, B, x, y\}, \delta, q_0, B, F \rangle$$
\(\Sigma = \{0, 1\}\)
Input accepts only binary digits (0 and 1)
Auxiliary symbols \(\{x, y\}\)
Used to mark processed bits (x=0, y=1)

💡 Operation Principle (Ripple Carry): The machine alternately reads the least significant bits from two numbers (right end). After reading a bit from the right number, it erases it, carries the value leftward, adds it to the corresponding position on the left, handles carry, and returns.

⚙️ Current State Panel

Current State
IDLE
Step
0
Read
-
BIN
ACTION LOG > Waiting for instructions...
Current Arithmetic Rule Set
\(q_0 \xrightarrow{0/1} R, \quad q_{add} \xrightarrow{Carry} L, \quad q_{return} \xrightarrow{Find \ Y} R\)