diff --git a/02_NumberRepresentation.ipynb b/02_NumberRepresentation.ipynb
index 6ac2a2a..8e36862 100644
--- a/02_NumberRepresentation.ipynb
+++ b/02_NumberRepresentation.ipynb
@@ -18,19 +18,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 84,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "9223372036854775807\n",
-      "True\n",
-      "9223372036854775808\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "import sys\n",
     "print (sys.maxsize)\n",
@@ -51,18 +41,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 85,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.6666666666666666\n",
-      "0\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "print (2/3)\n",
     "print (2//3)"
@@ -79,20 +60,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 86,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Binary representation of 18 : 0b10010\n",
-      "Hexadecimal representation of 18 : 0x12\n",
-      "Decimal representation of 0b10010 : 18\n",
-      "Decimal representation of 0x12 : 18\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# an integer in decimal representation\n",
     "a=18\n",
@@ -127,19 +97,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 87,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Logical AND  12\n",
-      "Logical OR  61\n",
-      "Logical XOR  49\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "a = 60            # 60 = 0011 1100 \n",
     "b = 13            # 13 = 0000 1101 \n",
@@ -163,17 +123,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 88,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Negation of a   -61\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "c = ~a;           # -61 = 1100 0011\n",
     "print (\"Negation of a  \", c)"
@@ -252,23 +204,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 89,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<img src=\"http://www.dspguide.com/graphics/F_4_2.gif\"/>"
-      ],
-      "text/plain": [
-       "<IPython.core.display.Image object>"
-      ]
-     },
-     "execution_count": 89,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "from IPython.display import Image\n",
     "Image(url='http://www.dspguide.com/graphics/F_4_2.gif')"
@@ -310,17 +248,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 90,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "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)\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "import sys\n",
     "print (sys.float_info)"
@@ -338,19 +268,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 91,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "7.00000000000001\n",
-      "7.000000000000001\n",
-      "7.0\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "for e in [14,15,16]: print (7+1.0*10**-e)"
    ]
@@ -369,27 +289,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 92,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.1\n"
-     ]
-    },
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 92,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# is 1/10 the same of 0.1?\n",
     "print (1/10)\n",
@@ -409,18 +311,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 93,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "3.141592653589793\n",
-      "0x1.921fb54442d18p+1\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "import math\n",
     "x=math.pi\n",
@@ -437,18 +330,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 96,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "3.1415926535898\n",
-      "1.00000000000000022\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "print (format(math.pi, '.13f'))  # give 13 significant digits\n",
     "\n",
@@ -466,18 +350,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 97,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1.1920928955078125e-07\n",
-      "1.1102230246251565e-16\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# 23 bits are used for f in single precision floating points \n",
     "print (2**-23)\n",
@@ -495,20 +370,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 98,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "0.0"
-      ]
-     },
-     "execution_count": 98,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "1 + 6.022e23 - 6.022e23"
    ]
@@ -522,18 +386,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 99,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "1.0\n",
-      "0.0\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "print (6.022e23 - 6.022e23 + 1)\n",
     "print (1 + 6.022e23 - 6.022e23)\n"
@@ -548,20 +403,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 100,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "False"
-      ]
-     },
-     "execution_count": 100,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "import math\n",
     "a = math.exp(1);\n",
@@ -572,18 +416,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 101,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.0\n",
-      "-1011.7261024082587\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# (we'll see numpy soon, bear with me for the moment)\n",
     "\n",
@@ -619,20 +454,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 102,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "t1 = 61249.00853150303\n",
-      "t2 = 158057.9134162482\n",
-      "% change in x = 0.0006366263894271296\n",
-      "% change in tan(x) = 158.05791343536953\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# The tangent function is poorly conditioned\n",
     "\n",
@@ -650,20 +474,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 103,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x11bd56908>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# Catastrophic cancellation occurs when subtracitng\n",
     "# two numbers that are very close to one another\n",
@@ -684,19 +497,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 104,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.999999999999999888977697537484\n",
-      "0.000000000000000111022302462516\n",
-      "0.917540\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# We know from L'Hopital's rule that the answer is 0.5 at 0\n",
     "# and should be very close to 0.5 throughout this tiny interval\n",
@@ -709,20 +512,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 105,
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "image/png": 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\n",
-      "text/plain": [
-       "<matplotlib.figure.Figure at 0x11be15080>"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# Numerically stable version of funtion using simple trignometry\n",
     "\n",
@@ -746,7 +538,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 106,
+   "execution_count": null,
    "metadata": {},
    "outputs": [],
    "source": [
@@ -777,20 +569,9 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 107,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "0.08239379980573168\n",
-      "0.0\n",
-      "0.08247527080374556\n",
-      "0.08177592628472322\n"
-     ]
-    }
-   ],
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# check the performances with an array \n",
     "# of randomly distributed data around 1e12\n",
diff --git a/02ex_NumberRepresentation.ipynb b/02ex_NumberRepresentation.ipynb
new file mode 100644
index 0000000..b03e2e5
--- /dev/null
+++ b/02ex_NumberRepresentation.ipynb
@@ -0,0 +1,104 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "1\\. Write a function that converts number representation (bin<->dec<->hex)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "2\\. Write a function that converts a 32 bit word into a single precision floating point (i.e. interprets the various bits as sign, mantissa and exponent)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "3\\. Write a program to determine the underflow and overflow limits (within a factor of 2) for python on your computer. \n",
+    "\n",
+    "**Tips**: define two variables inizialized to 1 and halve/double them enough time to exceed the under/over-flow limits  "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "4\\. Write a program to determine the machine precision\n",
+    "\n",
+    "**Tips**: define a new variable by adding a smaller and smaller value (proceeding similarly to prob. 2) to an original variable and check the point where the two are the same "
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "5\\. Write a function that takes in input three parameters $a$, $b$ and $c$ and prints out the two solutions to the quadratic equation $ax^2+bx+c=0$ using the standard formula:\n",
+    "$$\n",
+    "x=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}\n",
+    "$$\n",
+    "\n",
+    "(a) use the program to compute the solution for $a=0.001$, $b=1000$ and $c=0.001$\n",
+    "\n",
+    "(b) re-express the standard solution formula by multiplying top and bottom by $-b\\mp\\sqrt{b^2-4ac}$ and again find the solution for $a=0.001$, $b=1000$ and $c=0.001$. How does it compare with what previously obtained? Why?\n",
+    "\n",
+    "(c) write a function that compute the roots of a quadratic equation accurately in all cases"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "6\\. Write a program that implements a function $f(x)$ returning the value of $x(x−1)$\n",
+    "\n",
+    "(a)calculates the derivative of the function at the point $x = 1$ using the derivative definition:\n",
+    "\n",
+    "$$\n",
+    "\\frac{{\\rm d}f}{{\\rm d}x} = \\lim_{\\delta\\to0} \\frac{f(x+\\delta)-f(x)}{\\delta}\n",
+    "$$\n",
+    "\n",
+    "with δ = 10−2. Calculate the true value of the same derivative analytically and compare with the answer your program gives. The two will not agree perfectly. Why not?\n",
+    "\n",
+    "(b) Repeat the calculation for $\\delta = 10^{−4}, 10^{−6}, 10^{−8}, 10^{−10}, 10^{−12}$ and $10^{−14}$. How does the accuracy scales with $\\delta$?"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "7\\. Calculate the integral"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.5.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}