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questions.md

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+# Boolean questions
+
+Create the following variables.
+
+```
+a = Bits("11110000")
+b = Bits("10101010")
+```
+
+For each of the following bytes, give an equivalent 
+expression which uses only `a`, `b`, and bit operators.
+The answers to the first two questions are given.
+
+1. 01010101
+
+~b
+
+2. 00000101
+
+~a & ~b
+
+3. 00000001
+
+4. 10000000
+
+5. 01010000
+
+6. 00001010
+
+7. 01010000
+
+8. 10101011
+
+## Integer questions
+
+These questions are difficult! Try exploring ideas with `Bits` 
+in Terminal, a paper and pencil, and a whiteboard. And definitely
+talk with others.
+
+9. If `a` represents a positive integer, and `one = Bits(1, length=len(a))`, 
+   give an expression equivalent to `-a`, but which does not use negation.
+
+10. It is extremely easy to double a binary number: just shift all the bits 
+    to the left. (`a << 1` is twice `a`.) Explain why this trick works. 
+
+11. Consider the following: 
+   ```
+   >>> hundred = Bits(100, 8)
+   >>> hundred
+   01100100
+   >>> (hundred + hundred)
+   11001000
+   >>> (hundred + hundred).int
+   -56
+   ```
+   Apparently 100 + 100 = -56. What's going on here?
+
+12. What is the bit representation of negative zero? Explain your answer.
+
+13. What's the largest integer that can be represented in a single byte? 
+    Explain your reasoning.
+
+14. What's the smallest integer that can be represented in a single byte? 
+    Explain your reasoning.
+
+15. What's the largest integer that can be represented in `n` bits? 
+    Explain your reasoning.
+
+## Text questions
+
+16. Look at the bits for a few different characters using the `utf8` encoding. 
+    You will notice they have different bit lengths:
+
+    ```
+    >>> Bits('a', encoding='utf8')
+    01100001
+    >>> Bits('ñ', encoding='utf8')
+    1100001110110001
+    >>> Bits('♣', encoding='utf8')
+    111000101001100110100011
+    >>> Bits('😍', encoding='utf8')
+    11110000100111111001100010001101
+    ```
+    
+    When it's time to decode a sequence of utf8-encoded bits, the decoder
+    somehow needs to decide when it has read enough bits to decode a character, 
+    and when it needs to keep reading. For example, the decoder will produce 
+    'a' after reading 8 bits but after reading the first 8 bits of 'ñ', the 
+    decoder realizes it needs to read 8 more bits. 
+
+    Make a hypothesis about how this could work. 
+
+