generated from mwc/lab_encoding
134 lines
3.7 KiB
Markdown
134 lines
3.7 KiB
Markdown
# Nelson Mason
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# Boolean questions
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Create the following variables.
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```
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a = Bits("11110000")
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b = Bits("10101010")
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```
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For each of the following bytes, give an equivalent
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expression which uses only `a`, `b`, and bit operators.
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The answers to the first two questions are given.
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1. 01010101
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~b
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2. 00000101
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~a & ~b
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3. 00000001
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~a >> 3
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4. 10000000
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a << 3
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5. 01010000
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~b & a
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6. 00001010
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~a & b
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7. 01010000
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~b << 4
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8. 10101011
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~a >> 3 | b
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## Integer questions
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These questions are difficult! Try exploring ideas with `Bits`
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in Terminal, a paper and pencil, and a whiteboard. And definitely
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talk with others.
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9. If `a` represents a positive integer, and `one = Bits(1, length=len(a))`,
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give an expression equivalent to `-a`, but which does not use negation.
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>>>a=91
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>>>a
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01011011
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>>>one=Bits(1, 8)
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>>>one
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00000001
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>>>~a
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10100100
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**>>>~a + one**
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10100101
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>>>-a
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10100101
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>>>-a.int
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-91
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10. It is extremely easy to double a binary number: just shift all the bits
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to the left. (`a << 1` is twice `a`.) Explain why this trick works.
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Every binary digit place, from right to left, each left shift of one,
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raises the digit to the power of 2.
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11. Consider the following:
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```
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>>> hundred = Bits(100, 8)
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>>> hundred
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01100100
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>>> (hundred + hundred)
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11001000
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>>> (hundred + hundred).int
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-56
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```
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Apparently 100 + 100 = -56. What's going on here?
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The range of Bits in this case is from -128 to 128, in base 10. If you change the first line to: **hundred = Bits(100, 9)**, that ninth bit (on the left) increases the Bits range to from -256 to 256, in base 10. So, then you get the right answer: 200.
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12. What is the bit representation of negative zero? Explain your answer.
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"What is negative 0 in binary?
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In a 1+7-bit sign-and-magnitude representation for integers, negative zero is represented by the bit string 1000 0000 . In an 8-bit ones' complement representation, negative zero is represented by the bit string 1111 1111 . In all these three encodings, positive or unsigned zero is represented by 0000 0000 ." - Google Search
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13. What's the largest integer that can be represented in a single byte? (8 bits in a byte).
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Explain your reasoning. 127
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"For a signed integer (the most common representation in modern computing, using two's complement), the range is -128 to 127."
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- Google Search
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14. What's the smallest integer that can be represented in a single byte? (8 bits in a byte).
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Explain your reasoning. -128
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"For a signed integer (the most common representation in modern computing, using two's complement), the range is -128 to 127."
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- Google Search
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15. What's the largest integer that can be represented in `n` bits? ((2**n)/2) - 1.
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Explain your reasoning.
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Again, power of 2 for each bit, as you go to the left, one bit at a time.
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Also, the range of integers must include negative numbers, so you divide the total by 2.
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Then you subtract 1 because 0 is included in the range.
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## Text questions
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16. Look at the bits for a few different characters using the `utf8` encoding.
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You will notice they have different bit lengths:
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```
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>>> Bits('a', encoding='utf8')
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01100001
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>>> Bits('ñ', encoding='utf8')
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1100001110110001
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>>> Bits('♣', encoding='utf8')
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111000101001100110100011
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>>> Bits('😍', encoding='utf8')
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11110000100111111001100010001101
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```
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When it's time to decode a sequence of utf8-encoded bits, the decoder
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somehow needs to decide when it has read enough bits to decode a character,
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and when it needs to keep reading. For example, the decoder will produce
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'a' after reading 8 bits but after reading the first 8 bits of 'ñ', the
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decoder realizes it needs to read 8 more bits.
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Make a hypothesis about how this could work.
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