lab_encoding/questions.md

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.