{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "instructions = {\n",
    "    'NOP': ('0','0','0','0','0','0','0','0','0','0','0','0',),\n",
    "    'HLT': ('0','0','0','0','0','0','0','0','0','0','0','1',),\n",
    "    'BNZ': ('0','0','0','0','0','0','0','0','0','0','1','0',),\n",
    "    'BNA': ('0','0','0','0','0','0','0','0','0','0','1','1',),\n",
    "    'BNP': ('0','0','0','0','0','0','0','0','0','1','0','0',),\n",
    "    'BNN': ('0','0','0','0','0','0','0','0','0','1','0','1',),\n",
    "    'LOD': ('0','0','0','0','0','0','1','0','0','X','X','X',),\n",
    "    'STR': ('0','0','0','0','0','0','1','0','1','X','X','X',),\n",
    "    'POP': ('0','0','0','0','0','0','1','1','0','X','X','X',),\n",
    "    'PSH': ('0','0','0','0','0','0','1','1','1','X','X','X',),\n",
    "    'LIU': ('0','0','0','0','0','1','X','X','X','X','X','X',),\n",
    "    'LDI': ('0','0','0','0','1','0','X','X','X','X','X','X',),\n",
    "    'LIL': ('0','0','0','0','1','1','X','X','X','X','X','X',),\n",
    "    'LSH': ('0','0','0','1','0','0','X','X','X','X','X','X',),\n",
    "    'RSH': ('0','0','0','1','0','1','X','X','X','X','X','X',),\n",
    "    'INC': ('0','0','0','1','1','0','X','X','X','X','X','X',),\n",
    "    'DEC': ('0','0','0','1','1','1','X','X','X','X','X','X',),\n",
    "    'AND': ('0','0','1','X','X','X','X','X','X','X','X','X',),\n",
    "    'OR':  ('0','1','0','X','X','X','X','X','X','X','X','X',),\n",
    "    'SUB': ('0','1','1','X','X','X','X','X','X','X','X','X',),\n",
    "    'XOR': ('1','0','0','X','X','X','X','X','X','X','X','X',),\n",
    "    'NAD': ('1','0','1','X','X','X','X','X','X','X','X','X',),\n",
    "    'NOR': ('1','1','0','X','X','X','X','X','X','X','X','X',),\n",
    "    'ADD': ('1','1','1','X','X','X','X','X','X','X','X','X',),\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "controls = {\n",
    "    'Halt': ['HLT'],\n",
    "    'Branch if Zero': ['BNZ'],\n",
    "    'Branch if Not Zero': ['BNA'],\n",
    "    'Branch if Positive': ['BNP'],\n",
    "    'Branch if Negative': ['BNN'],\n",
    "    'Read Memory': ['LOD','POP'],\n",
    "    'Write Memory': ['STR','PSH'],\n",
    "    'Use Memory Pointer': ['LOD','STR'],\n",
    "    'Use Stack Pointer': ['PSH','POP'],\n",
    "    'Load Immediate Upper': ['LIU'],\n",
    "    'Load Immediate Lower': ['LDI'],\n",
    "    'Load Immediate Lower OR': ['LIL'],\n",
    "    'Left Shift': ['LSH'],\n",
    "    'Right Shift': ['RSH'],\n",
    "    'AND': ['AND','NAD'],\n",
    "    'OR': ['OR','NOR'],\n",
    "    'XOR': ['XOR'],\n",
    "    'NOT out': ['NAD','NOR'],\n",
    "    'NOT Reg 3': ['DEC','SUB'],\n",
    "    'Add': ['INC','DEC','SUB','ADD'],\n",
    "    'Inject Carry': ['INC','DEC','SUB'],\n",
    "    'One as Reg 3': ['DEC'],\n",
    "    'Write Reg 1': ['LOD','PSH','LSH','RSH','INC','DEC','AND','OR','SUB','XOR','NAD','NOR','ADD'],\n",
    "    'Read Reg 1': ['STR','POP'],\n",
    "    'Any Reg 1': ['LOD','PSH','LSH','RSH','INC','DEC','AND','OR','SUB','XOR','NAD','NOR','ADD','STR','POP'],\n",
    "    'Read Reg 2': ['LSH','RSH','INC','DEC','AND','OR','SUB','XOR','NAD','NOR','ADD'],\n",
    "    'Read Reg 3': ['AND','OR','SUB','XOR','NAD','NOR','ADD'],\n",
    "    'Update Flags': ['LSH','RSH','INC','DEC','AND','OR','SUB','XOR','NAD','NOR','ADD'],\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simplifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Halt (ORG) = A & ~B & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Halt (CNF) = A & ~B & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Halt (DNF) = A & ~B & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Branch if Zero (ORG) = B & ~A & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Zero (CNF) = B & ~A & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Zero (DNF) = B & ~A & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Branch if Not Zero (ORG) = A & B & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Not Zero (CNF) = A & B & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Not Zero (DNF) = A & B & ~C & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Branch if Positive (ORG) = C & ~A & ~B & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Positive (CNF) = C & ~A & ~B & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Positive (DNF) = C & ~A & ~B & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Branch if Negative (ORG) = A & C & ~B & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Negative (CNF) = A & C & ~B & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Branch if Negative (DNF) = A & C & ~B & ~D & ~E & ~F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Read Memory (ORG) = (E & F & ~D & ~G & ~H & ~I & ~J & ~K & ~L) | (F & ~D & ~E & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Read Memory (CNF) = F & ~D & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Read Memory (DNF) = F & ~D & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Write Memory (ORG) = (D & E & F & ~G & ~H & ~I & ~J & ~K & ~L) | (D & F & ~E & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Write Memory (CNF) = D & F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Write Memory (DNF) = D & F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Use Memory Pointer (ORG) = (D & F & ~E & ~G & ~H & ~I & ~J & ~K & ~L) | (F & ~D & ~E & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Use Memory Pointer (CNF) = F & ~E & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Use Memory Pointer (DNF) = F & ~E & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Use Stack Pointer (ORG) = (D & E & F & ~G & ~H & ~I & ~J & ~K & ~L) | (E & F & ~D & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Use Stack Pointer (CNF) = E & F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Use Stack Pointer (DNF) = E & F & ~G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Load Immediate Upper (ORG) = G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Load Immediate Upper (CNF) = G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Load Immediate Upper (DNF) = G & ~H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Load Immediate Lower (ORG) = H & ~G & ~I & ~J & ~K & ~L\n",
      "\n",
      "Load Immediate Lower (CNF) = H & ~G & ~I & ~J & ~K & ~L\n",
      "\n",
      "Load Immediate Lower (DNF) = H & ~G & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Load Immediate Lower OR (ORG) = G & H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Load Immediate Lower OR (CNF) = G & H & ~I & ~J & ~K & ~L\n",
      "\n",
      "Load Immediate Lower OR (DNF) = G & H & ~I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Left Shift (ORG) = I & ~G & ~H & ~J & ~K & ~L\n",
      "\n",
      "Left Shift (CNF) = I & ~G & ~H & ~J & ~K & ~L\n",
      "\n",
      "Left Shift (DNF) = I & ~G & ~H & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Right Shift (ORG) = G & I & ~H & ~J & ~K & ~L\n",
      "\n",
      "Right Shift (CNF) = G & I & ~H & ~J & ~K & ~L\n",
      "\n",
      "Right Shift (DNF) = G & I & ~H & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "AND (ORG) = (J & L & ~K) | (J & ~K & ~L)\n",
      "\n",
      "AND (CNF) = J & ~K\n",
      "\n",
      "AND (DNF) = J & ~K\n",
      "\n",
      "\n",
      "\n",
      "OR (ORG) = (K & L & ~J) | (K & ~J & ~L)\n",
      "\n",
      "OR (CNF) = K & ~J\n",
      "\n",
      "OR (DNF) = K & ~J\n",
      "\n",
      "\n",
      "\n",
      "XOR (ORG) = L & ~J & ~K\n",
      "\n",
      "XOR (CNF) = L & ~J & ~K\n",
      "\n",
      "XOR (DNF) = L & ~J & ~K\n",
      "\n",
      "\n",
      "\n",
      "NOT out (ORG) = (J & L & ~K) | (K & L & ~J)\n",
      "\n",
      "NOT out (CNF) = L & (J | K) & (~J | ~K)\n",
      "\n",
      "NOT out (DNF) = (J & L & ~K) | (K & L & ~J)\n",
      "\n",
      "\n",
      "\n",
      "NOT Reg 3 (ORG) = (J & K & ~L) | (G & H & I & ~J & ~K & ~L)\n",
      "\n",
      "NOT Reg 3 (CNF) = ~L & (G | J) & (H | J) & (I | J) & (J | ~K) & (K | ~J)\n",
      "\n",
      "NOT Reg 3 (DNF) = (J & K & ~L) | (G & H & I & ~J & ~K & ~L)\n",
      "\n",
      "\n",
      "\n",
      "Add (ORG) = (J & K & L) | (J & K & ~L) | (G & H & I & ~J & ~K & ~L) | (H & I & ~G & ~J & ~K & ~L)\n",
      "\n",
      "Add (CNF) = (H | J) & (I | J) & (J | ~K) & (J | ~L) & (K | ~J)\n",
      "\n",
      "Add (DNF) = (J & K) | (H & I & ~J & ~K & ~L)\n",
      "\n",
      "\n",
      "\n",
      "Inject Carry (ORG) = (J & K & ~L) | (G & H & I & ~J & ~K & ~L) | (H & I & ~G & ~J & ~K & ~L)\n",
      "\n",
      "Inject Carry (CNF) = ~L & (H | J) & (I | J) & (J | ~K) & (K | ~J)\n",
      "\n",
      "Inject Carry (DNF) = (J & K & ~L) | (H & I & ~J & ~K & ~L)\n",
      "\n",
      "\n",
      "\n",
      "One as Reg 3 (ORG) = G & H & I & ~J & ~K & ~L\n",
      "\n",
      "One as Reg 3 (CNF) = G & H & I & ~J & ~K & ~L\n",
      "\n",
      "One as Reg 3 (DNF) = G & H & I & ~J & ~K & ~L\n",
      "\n",
      "\n",
      "\n",
      "Write Reg 1 (ORG) = (J & K & L) | (J & K & ~L) | (J & L & ~K) | (K & L & ~J) | (J & ~K & ~L) | (K & ~J & ~L) | (L & ~J & ~K) | (G & H & I & ~J & ~K & ~L) | (G & I & ~H & ~J & ~K & ~L) | (H & I & ~G & ~J & ~K & ~L) | (I & ~G & ~H & ~J & ~K & ~L) | (D & E & F & ~G & ~H & ~I & ~J & ~K & ~L) | (F & ~D & ~E & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Write Reg 1 (CNF) = (F | I | J | K | L) & (I | J | K | L | ~G) & (I | J | K | L | ~H) & (D | I | J | K | L | ~E) & (E | I | J | K | L | ~D)\n",
      "\n",
      "Write Reg 1 (DNF) = I | J | K | L | (D & E & F & ~G & ~H) | (F & ~D & ~E & ~G & ~H)\n",
      "\n",
      "\n",
      "\n",
      "Read Reg 1 (ORG) = (D & F & ~E & ~G & ~H & ~I & ~J & ~K & ~L) | (E & F & ~D & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Read Reg 1 (CNF) = F & ~G & ~H & ~I & ~J & ~K & ~L & (D | E) & (~D | ~E)\n",
      "\n",
      "Read Reg 1 (DNF) = (D & F & ~E & ~G & ~H & ~I & ~J & ~K & ~L) | (E & F & ~D & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "\n",
      "\n",
      "Any Reg 1 (ORG) = (J & K & L) | (J & K & ~L) | (J & L & ~K) | (K & L & ~J) | (J & ~K & ~L) | (K & ~J & ~L) | (L & ~J & ~K) | (G & H & I & ~J & ~K & ~L) | (G & I & ~H & ~J & ~K & ~L) | (H & I & ~G & ~J & ~K & ~L) | (I & ~G & ~H & ~J & ~K & ~L) | (D & E & F & ~G & ~H & ~I & ~J & ~K & ~L) | (D & F & ~E & ~G & ~H & ~I & ~J & ~K & ~L) | (E & F & ~D & ~G & ~H & ~I & ~J & ~K & ~L) | (F & ~D & ~E & ~G & ~H & ~I & ~J & ~K & ~L)\n",
      "\n",
      "Any Reg 1 (CNF) = (F | I | J | K | L) & (I | J | K | L | ~G) & (I | J | K | L | ~H)\n",
      "\n",
      "Any Reg 1 (DNF) = I | J | K | L | (F & ~G & ~H)\n",
      "\n",
      "\n",
      "\n",
      "Read Reg 2 (ORG) = (J & K & L) | (J & K & ~L) | (J & L & ~K) | (K & L & ~J) | (J & ~K & ~L) | (K & ~J & ~L) | (L & ~J & ~K) | (G & H & I & ~J & ~K & ~L) | (G & I & ~H & ~J & ~K & ~L) | (H & I & ~G & ~J & ~K & ~L) | (I & ~G & ~H & ~J & ~K & ~L)\n",
      "\n",
      "Read Reg 2 (CNF) = I | J | K | L\n",
      "\n",
      "Read Reg 2 (DNF) = I | J | K | L\n",
      "\n",
      "\n",
      "\n",
      "Read Reg 3 (ORG) = (J & K & L) | (J & K & ~L) | (J & L & ~K) | (K & L & ~J) | (J & ~K & ~L) | (K & ~J & ~L) | (L & ~J & ~K)\n",
      "\n",
      "Read Reg 3 (CNF) = J | K | L\n",
      "\n",
      "Read Reg 3 (DNF) = J | K | L\n",
      "\n",
      "\n",
      "\n",
      "Update Flags (ORG) = (J & K & L) | (J & K & ~L) | (J & L & ~K) | (K & L & ~J) | (J & ~K & ~L) | (K & ~J & ~L) | (L & ~J & ~K) | (G & H & I & ~J & ~K & ~L) | (G & I & ~H & ~J & ~K & ~L) | (H & I & ~G & ~J & ~K & ~L) | (I & ~G & ~H & ~J & ~K & ~L)\n",
      "\n",
      "Update Flags (CNF) = I | J | K | L\n",
      "\n",
      "Update Flags (DNF) = I | J | K | L\n",
      "\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sympy import symbols, Not, And, Or, simplify_logic\n",
    "\n",
    "A, B, C, D, E, F, G, H, I, J, K, L = symbols('A B C D E F G H I J K L')\n",
    "\n",
    "def equ_s(control: list[str]):\n",
    "    inputs =  [A, B, C, D, E, F, G, H, I, J, K, L]\n",
    "    equ = []\n",
    "\n",
    "    for instruction in control:\n",
    "        sub_equ = []\n",
    "        for i, bit in enumerate(reversed(instructions[instruction])):\n",
    "            if bit == '0':\n",
    "                sub_equ.append(Not(inputs[i]))\n",
    "            elif bit == '1':\n",
    "                sub_equ.append(inputs[i])\n",
    "        equ.append(And(*sub_equ))\n",
    "\n",
    "    return Or(*equ)\n",
    "\n",
    "for key, value in controls.items():\n",
    "    expr = equ_s(value)\n",
    "    cnf_expr = simplify_logic(expr, form='cnf', force=True)\n",
    "    dnf_expr = simplify_logic(expr, form='dnf', force=True)\n",
    "    print(key, '(ORG) =', expr, end='\\n\\n')\n",
    "    print(key, '(CNF) =', cnf_expr, end='\\n\\n')\n",
    "    print(key, '(DNF) =', dnf_expr, end='\\n\\n\\n\\n')"
   ]
  }
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