XOR example.ipynb

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   "source": [
    "# Python bitwise XOR (exclusive OR)\n",
    "\n",
    "The `^` operator does a bitwise XOR.\n",
    "\n",
    "That explains the weird example we saw in the notebook today.\n",
    "\n",
    "Here is the example again."
   ]
  },
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   "cell_type": "code",
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   "metadata": {},
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   "source": [
    "x = [1, 2, 3, 4, 5]"
   ]
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     "data": {
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       "[1, 2, 3, 4, 5]"
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    "x"
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     "data": {
      "text/plain": [
       "[3, 0, 1, 6, 7]"
      ]
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     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "[x^2 for x in x]"
   ]
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   "cell_type": "markdown",
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   "source": [
    "WTF? I thought I was squaring each number.\n",
    "\n",
    "Instead I was taking the XOR of each number with 2.\n",
    "\n",
    "Below we can see what was happening.\n",
    "\n",
    "First let's see the x values as binary."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['0001', '0010', '0011', '0100', '0101']"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[format(x, '04b') for x in x]"
   ]
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   "source": [
    "Here is 2 repeated 5 times in binary, followed by the XOR of x with 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['0010', '0010', '0010', '0010', '0010']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[format(2, '04b') for x in x]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['0011', '0000', '0001', '0110', '0111']"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[format(x^2, '04b') for x in x]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can verify that each value really is the exclusive OR of the bits from the original list."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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