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completes the questions in questions.md for the encoding lab

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erbrown2
2026-05-17 21:00:40 -04:00
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@@ -20,17 +20,24 @@ The answers to the first two questions are given.
~a & ~b
3. 00000001
~a & b
4. 10000000
a & (b ^ b)
5. 01010000
a & ~b
6. 00001010
~a & b
7. 01010000
a & ~b
8. 10101011
b | (~a & ~b)
## Integer questions
These questions are difficult! Try exploring ideas with `Bits`
@@ -40,9 +47,13 @@ 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.
~a + one
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.
Every bit position represents a power of 2. Shifting all bits one place to the left multiplies every bit's value by 2.
11. Consider the following:
```
>>> hundred = Bits(100, 8)
@@ -55,16 +66,25 @@ talk with others.
```
Apparently 100 + 100 = -56. What's going on here?
100 + 100 = 200 in bit it is 11001000. Because the first is 1 the bit represents a negative number -56.
12. What is the bit representation of negative zero? Explain your answer.
There is no negative zero zero is only represented by 00000000.
13. What's the largest integer that can be represented in a single byte?
Explain your reasoning.
127 is the largest because the first 1 represents a negative hence 01111111 = 127
14. What's the smallest integer that can be represented in a single byte?
Explain your reasoning.
-128 is the smallest where the smallest is 10000000.
15. What's the largest integer that can be represented in `n` bits?
Explain your reasoning.
2^(n-1) -1 : one bit is used for the sign example if n = 3 bits then it would be 2^2 - 1 = 3 leading to 011.
## Text questions
@@ -90,4 +110,6 @@ talk with others.
Make a hypothesis about how this could work.
Use the leading bits of the first byte to indicate the total length of the characters where 0--------- = 1 byte "a" then 110------- = 2 byte "n" characters, 1110------ = 3 byte, shade characters then each byte has specific meaning as used above.