Lec_06_code_data.ipynb

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    "%%html\n",
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   "source": [
    "# CS 121 Lecture 6 : Code and data"
   ]
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  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
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     "slide_type": "skip"
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   "source": [
    "# utility code \n",
    "%run \"Utilities.ipynb\"\n",
    "from IPython.display import clear_output\n",
    "clear_output()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "source": [
    "def AND(a,b): return a*b\n",
    "\n",
    "def OR(a,b): return 1 if a+b else 0\n",
    "\n",
    "def NOT(a): return 1-a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
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   "source": [
    "def IF(cond,a,b):\n",
    "    notcond = NAND(cond,cond)\n",
    "    temp = NAND(b,notcond)\n",
    "    temp1 = NAND(a,cond)\n",
    "    return NAND(temp,temp1)\n",
    "mystery = circuit2prog(circuit(IF))"
   ]
  },
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   "execution_count": 8,
   "metadata": {
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     "text": [
      "gate_0 = NAND(X[0],X[0])\n",
      "gate_1 = NAND(X[2],gate_0)\n",
      "gate_2 = NAND(X[1],X[0])\n",
      "Y[0] = NAND(gate_1,gate_2)\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# What function does the following NAND-CIRC program compute?\n",
    "print(mystery)"
   ]
  },
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   "source": [
    "circuit(mystery)"
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  {
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   "metadata": {
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   },
   "source": [
    "## Sugar all the way "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
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   "outputs": [],
   "source": [
    "def NOT(a): return NAND(a,a)\n",
    "def AND(a,b): return NOT(NAND(a,b))\n",
    "def OR(a,b): return NAND(NOT(a),NOT(b))"
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   "execution_count": null,
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   "source": [
    "GLOBAL_NANDONLY = True"
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   "metadata": {
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    "def MAJ(a,b,c):\n",
    "    u = NAND(a,b)\n",
    "    v = NAND(a,c)\n",
    "    w = NAND(b,c)\n",
    "    z = NAND(u,v)\n",
    "    return NAND(w,NOT(z))"
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   "source": [
    "def XOR(a,b):\n",
    "    u = NAND(a,b)\n",
    "    v = NAND(a,u)\n",
    "    w = NAND(b,u)\n",
    "    return NAND(v,w)\n",
    "\n",
    "def XOR3(a,b,c):\n",
    "    return XOR(XOR(a,b),c)"
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      "text/plain": [
       "<Figure size 458.455x257.757 with 1 Axes>"
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     },
     "metadata": {
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   ],
   "source": [
    "def ADD1(a,b):\n",
    "    return AND(a,b),XOR(a,b)\n",
    "\n",
    "circuit(ADD1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1, 1, 0]"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def addnumbers(X,Y):\n",
    "    n = len(X)\n",
    "    Z = [0]*(n+1)\n",
    "    carry = zero(X[0])\n",
    "    for i in range(n-1,-1,-1):\n",
    "        Z[i+1] = XOR3(X[i],Y[i],carry)\n",
    "        carry = MAJ(carry,X[i],Y[i])\n",
    "    Z[0] = carry\n",
    "    return Z\n",
    "\n",
    "addnumbers([1,1],[1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": []
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
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    "add2circ = circuit(addnumbers,2,2)\n",
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    }
   ],
   "source": [
    "X = list(range(10,50,5))\n",
    "Y = [circuit(addnumbers,n,n).size() for n in X]\n",
    "import matplotlib.pyplot as plt\n",
    "plt.plot(X,Y)\n",
    "plt.ylabel('circuit size')\n",
    "plt.xlabel('input length')\n",
    "plt.show()"
   ]
  }
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