questions.md

.envrc

@@ -0,0 +1 @@
+source .venv/bin/activate

questions.md

@@ -21,16 +21,28 @@ The answers to the first two questions are given.
 
 3. 00000001
 
+~a >> 3
+
 4. 10000000
 
+a << 3
+
 5. 01010000
 
+~b & a
+
 6. 00001010
 
+~a & b
+
 7. 01010000
 
+~b << 4
+
 8. 10101011
 
+~a >> 3 | b
+
 ## Integer questions
 
 These questions are difficult! Try exploring ideas with `Bits` 
@@ -40,8 +52,25 @@ 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=91
+>>>a
+01011011
+>>>one=Bits(1, 8)
+>>>one
+00000001
+>>>~a
+10100100
+**>>>~a + one**
+10100101
+>>>-a
+10100101
+>>>-a.int
+-91
+
 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 binary digit place, from right to left, each left shift of one, 
+    raises the digit to the power of 2.
 
 11. Consider the following: 
    ```
@@ -54,17 +83,27 @@ talk with others.
    -56
    ```
    Apparently 100 + 100 = -56. What's going on here? 
+   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.
 
 12. What is the bit representation of negative zero? Explain your answer.
+"What is negative 0 in binary?
+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
 
-13. What's the largest integer that can be represented in a single byte? 
+13. What's the largest integer that can be represented in a single byte? (8 bits in a byte).
-    Explain your reasoning.
+    Explain your reasoning. 127
+   "For a signed integer (the most common representation in modern computing, using two's complement), the range is -128 to 127."
+   - Google Search
 
-14. What's the smallest integer that can be represented in a single byte? 
+14. What's the smallest integer that can be represented in a single byte? (8 bits in a byte).
-    Explain your reasoning.
+    Explain your reasoning. -128
+    "For a signed integer (the most common representation in modern computing, using two's complement), the range is -128 to 127."
+   - Google Search
 
-15. What's the largest integer that can be represented in `n` bits? 
+15. What's the largest integer that can be represented in `n` bits? ((2**n)/2) - 1.
     Explain your reasoning.
+    Again, power of 2 for each bit, as you go to the left, one bit at a time.
+    Also, the range of integers must include negative numbers, so you divide the total by 2. 
+    Then you subtract 1 because 0 is included in the range.
 
 ## Text questions