02-python-essentials/02.03-numbers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 数字"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 整型 Integers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "整型运算，加减乘："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 + 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-1"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3 - 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "4 * 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在**Python 2.7**中，整型的运算结果只能返回整型，**除法**的结果也不例外。\n",
    "\n",
    "例如`12 / 5`返回的结果并不是2.4，而是2："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12 / 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "幂指数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2 ** 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "取余："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "32 % 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "赋值给变量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1\n",
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用`type()`函数来查看变量类型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "整型数字的最大最小值：\n",
    "\n",
    "在 32 位系统中，一个整型 4 个字节，最小值 `-2,147,483,648`，最大值 `2,147,483,647`。\n",
    "\n",
    "在 64 位系统中，一个整型 8 个字节，最小值 `-9,223,372,036,854,775,808`，最大值 `9,223,372,036,854,775,807`。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2147483647"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "sys.maxint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 长整型 Long Integers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当整型超出范围时，**Python**会自动将整型转化为长整型，不过长整型计算速度会比整型慢。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<type 'long'>\n"
     ]
    }
   ],
   "source": [
    "a = sys.maxint + 1\n",
    "print type(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "长整型的一个标志是后面以字母L结尾："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2147483648L"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以在赋值时强制让类型为长整型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "long"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "b = 1234L\n",
    "type(b)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "长整型可以与整型在一起进行计算，返回的类型还是长整型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2147483644L"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a - 4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 浮点数 Floating Point Numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "float"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1.4\n",
    "type(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在之前的除法例子`12 / 5`中，假如想要使返回的结果为2.4，可以将它们写成浮点数的形式："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12.0 / 5.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12 / 5.0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false,
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.4"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12.0 / 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上面的例子说明，浮点数与整数进行运算时，返回的仍然是浮点数："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.4"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "5 + 2.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "浮点数也可以进行与整数相似的运算，甚至可以取余："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.19999999999999973"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3.4 - 3.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "44.7"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12.3 + 32.4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.25"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "2.5 ** 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2999999999999998"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "3.4 % 2.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Python**的浮点数标准与**C**，**Java**一致，都是[IEEE 754 floating point standard](http://en.wikipedia.org/wiki/IEEE_floating_point)。\n",
    "\n",
    "注意看 `3.4 - 3.2` 的结果并不是我们预期的`0.2`，这是因为浮点数本身储存方式引起的，浮点数本身会存在一点误差。\n",
    "\n",
    "事实上，**Python** 中储存的值为'0.199999999999999733546474089962430298328399658203125'，因为这是最接近0.2的浮点数。|"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'0.199999999999999733546474089962430298328399658203125'"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "'{:.52}'.format(3.4 - 3.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "当我们使用`print`显示时，**Python**会自动校正这个结果"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2\n"
     ]
    }
   ],
   "source": [
    "print 3.4 - 3.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以用`sys.float_info`来查看浮点数的信息："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sys.float_info(max=1.7976931348623157e+308, max_exp=1024, max_10_exp=308, min=2.2250738585072014e-308, min_exp=-1021, min_10_exp=-307, dig=15, mant_dig=53, epsilon=2.220446049250313e-16, radix=2, rounds=1)"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import sys\n",
    "sys.float_info"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "例如浮点数能表示的最大值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.7976931348623157e+308"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.float_info.max"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "浮点数能表示的最接近0的值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2250738585072014e-308"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.float_info.min"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "浮点数的精度："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.220446049250313e-16"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sys.float_info.epsilon"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 复数 Complex Numbers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Python** 使用 `j` 来表示复数的虚部："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "complex"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a = 1 + 2j\n",
    "type(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以查看它的实部，虚部以及共轭："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.real"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.imag"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1-2j)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a.conjugate()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##交互计算"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以将复杂的表达式放在一起计算："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-27"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1 + 2 - (3 * 4 / 6) ** 5 + 7 % 5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "在**Python**中运算是有优先级的，优先级即算术的先后顺序，比如“先乘除后加减”和“先算括号里面的”都是两种优先级的规则，优先级从高到低排列如下：\n",
    "\n",
    "- `( )` 括号\n",
    "- `**` 幂指数运算\n",
    "- `* / // %` 乘，除，整数除法，取余运算\n",
    "- '+ -' 加减\n",
    "\n",
    "整数除法，返回的是比结果小的最大整数值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12.3 // 5.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-4.0"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "12.3 // -4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 简单的数学函数"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "绝对值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "12.4"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "abs(-12.4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "取整："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.0"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "round(21.6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "最大最小值："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "print min(2, 3, 4, 5)\n",
    "print max(2, 4, 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 变量名覆盖"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不要用内置的函数来命名变量，否则会出现意想不到的结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "builtin_function_or_method"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(max)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "不要这样做！！！"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "int"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max = 1\n",
    "type(max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "'int' object is not callable",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-41-c60446be959c>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mmax\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;36m4\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;36m5\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m: 'int' object is not callable"
     ]
    }
   ],
   "source": [
    "max(4, 5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 类型转换"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "浮点数转整型，只保留整数部分："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "12\n",
      "-3\n"
     ]
    }
   ],
   "source": [
    "print int(12.324)\n",
    "print int(-3.32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "整型转浮点型："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2\n"
     ]
    }
   ],
   "source": [
    "print float(1.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 其他表示"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "除了10进制外，整数还有其他类型的表示方法。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "科学计数法："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1e-06"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "1e-6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "16进制，前面加`0x`修饰，后面使用数字0-9A-F："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "255"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0xFF"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "8进制，前面加`0`或者`0o`修饰，后面使用数字0-7："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "55"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "067"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2进制，前面加`0b`修饰，后面使用数字0或1："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "42"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0b101010"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 原地计算 In-place"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Python**可以使用下面的形式进行原地计算："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "4.5\n",
      "9.0\n",
      "6.0\n"
     ]
    }
   ],
   "source": [
    "b = 2.5\n",
    "b += 2\n",
    "print b\n",
    "b *= 2\n",
    "print b\n",
    "b -= 3\n",
    "print b"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 布尔型 Boolean Data Type"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "布尔型可以看成特殊的二值变量，其取值为`True`和`False`："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "bool"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "q = True\n",
    "type(q)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "可以用表达式构建布尔型变量："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "False\n"
     ]
    }
   ],
   "source": [
    "q = 1 > 2\n",
    "print q"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "常用的比较符号包括：\n",
    "\n",
    "    <, >, <=, >=, ==, !=\n",
    "\n",
    "**Python**支持链式比较："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x = 2 \n",
    "1 < x <= 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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