Updates

modules/number_system/twos_complement.py

@@ -2,10 +2,15 @@ import random
 import sympy as sp
 
 title = "2's Complement Questions"
-description = "This module explains the 2's complement method for representing negative numbers."
+description = "This module explains the 2's complement method for representing negative numbers. The number of bits used for 2's complement calculations can vary."
 
-def generate_question():
-    number = ''.join(random.choice('01') for _ in range(8))
+def generate_question(num_bits):
+    # Ensure num_bits is a positive integer
+    if num_bits <= 0:
+        raise ValueError("Number of bits must be a positive integer.")
+    
+    # Generate a random binary number with the given number of bits
+    number = ''.join(random.choice('01') for _ in range(num_bits))
 
     def calculate_twos_complement(number):
         # Calculate 1's complement
@@ -13,7 +18,7 @@ def generate_question():
         
         # Calculate 2's complement
         twos_complement = bin(int(ones_complement, 2) + 1)[2:]
-        twos_complement = twos_complement.zfill(len(number))
+        twos_complement = twos_complement.zfill(num_bits)
         
         return ones_complement, twos_complement
 
@@ -22,13 +27,13 @@ def generate_question():
 
     # Generate incorrect answers
     while len(options) < 4:
-        invalid_number = ''.join(random.choice('01') for _ in range(8))
+        invalid_number = ''.join(random.choice('01') for _ in range(num_bits))
         if invalid_number != correct_answer:
             options.append(invalid_number)
     
     random.shuffle(options)
     
-    question = f"What is the 2's complement of the binary number {number}?"
+    question = f"What is the 2's complement of the binary number {number} (using {num_bits} bits)?"
     
     # Generate a step-by-step solution using SymPy
     num_expr = sp.sympify(f'0b{number}')
@@ -39,11 +44,11 @@ def generate_question():
         f"Step 1: Start with the original binary number: {number}",
         f"Step 2: Find the 1's complement by flipping all bits: {ones_complement}",
         f"Step 3: Add 1 to the 1's complement:",
-        f"        {ones_complement} + 1 = {bin(twos_expr)[2:].zfill(len(number))}",
+        f"        {ones_complement} + 1 = {bin(twos_expr)[2:].zfill(num_bits)}",
         f"Step 4: The 2's complement of {number} is {correct_answer}."
     ]
     
-    explanation = f"The 2's complement of {number} is {correct_answer}. It is calculated by inverting the bits and adding 1."
+    explanation = f"The 2's complement of {number} is {correct_answer}. It is calculated by inverting the bits and adding 1. Note that this calculation is performed using {num_bits} bits."
 
     return {
         "question": question,
@@ -52,3 +57,19 @@ def generate_question():
         "explanation": explanation,
         "step_by_step_solution": step_by_step_solution
     }
+
+# Example usage
+num_bits_list = [4, 8, 16]
+questions = {num_bits: generate_question(num_bits) for num_bits in num_bits_list}
+
+# Display the generated questions and their descriptions
+for num_bits, q in questions.items():
+    print(f"Number of bits: {num_bits}")
+    print("Question:", q["question"])
+    print("Options:", q["options"])
+    print("Correct Answer:", q["correct_answer"])
+    print("Explanation:", q["explanation"])
+    print("Step-by-Step Solution:")
+    for step in q["step_by_step_solution"]:
+        print(step)
+    print("\n" + "-"*40 + "\n")