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   "source": [
    "San Vu Ngoc - [IRMAR](https://irmar.univ-rennes1.fr/)\n",
    "___"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Écriture en base $b$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Quel est le nombre qui s'écrit \"5616\" en base 7 ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "int(\"5620\",7)"
   ]
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "(((5)  *7 + 6) *7 +  2 ) *7  + 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   "outputs": [],
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    "bin(2023)"
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "hex(2023)"
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice: Algorithme de Horner\n",
    "\n",
    "étant donnés la base $b$ et les coefficients $c_0$, ... , $c_k$, calculer l'entier correspondant, soit\n",
    "$$ n = c_k b^k + c_{k-1}b^{k-1} + \\cdots + c_1 b + c_0 $$\n",
    "**sans** calculer les puissances $b^j$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "oct(2023)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "int(\"3747\", 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "int(\"31043\",5)"
   ]
  }
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