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I answered the questions for both booleans and integers

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ambreenn
2026-04-10 12:32:40 -04:00
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@@ -12,24 +12,28 @@ 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
a >> 7
4. 10000000
a << 3
5. 01010000
a & ~b
6. 00001010
~a & b
7. 01010000
a & ~b
8. 10101011
b | (a >> 7)
## Integer questions
@@ -40,8 +44,11 @@ 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.
This trick works because every spot to the left is double of the right so moving everything will double the entire number
11. Consider the following:
```
@@ -55,16 +62,27 @@ talk with others.
```
Apparently 100 + 100 = -56. What's going on here?
the full 8-bit is equal to 256 so 200 mod 256 is the same as -56 mod 256
12. What is the bit representation of negative zero? Explain your answer.
zero is neither negative or positive, it is just the absence of a value so it would just be 00000000
13. What's the largest integer that can be represented in a single byte?
Explain your reasoning.
the largest integer that can be represented by a single byte is 127.
A byte is 8 bits, since the very left bit is positive with a 0, the highest representation would be 01111111 which is equal to 127
14. What's the smallest integer that can be represented in a single byte?
Explain your reasoning.
The smallest integer that can be represented by a single byte is -128.
Similar to problem 13, to have the smallest integer we need the largest negative number which is only represented by the very left number.
Therefore it would be 10000000 because we are not adding any positives to it.
15. What's the largest integer that can be represented in `n` bits?
Explain your reasoning.
The largest integer that can be represented in n bits is 2^(n-1) -1. Based on the example in 13 this pattern makes sense,
we have to do n-1 because the first number is negative and can not represent a positive integer. We also have to subtract 1
because it is one less.
## Text questions