Updates

modules/number_system/twos_complement.py

@@ -1,3 +1,5 @@
+# modules/number_system/twos_complement.py
+
 import random
 import sympy as sp
 
@@ -5,45 +7,47 @@ title = "2's Complement Questions"
 description = "This module explains the 2's complement method for representing negative numbers."
 
 def generate_question():
-    # Choose a random bit length from 4, 5, 6, and 8 bits
-    bit_lengths = [4, 5, 6, 8]
-    bit_length = random.choice(bit_lengths)
-
-    # Generate a random binary number of the selected bit length
-    number = ''.join(random.choice('01') for _ in range(bit_length))
-
-    def calculate_twos_complement(number):
-        ones_complement = ''.join('1' if bit == '0' else '0' for bit in number)
+    bit_lengths = [4, 5, 6, 7, 8]
+    num_bits = random.choice(bit_lengths)
+    
+    def generate_binary_number(length):
+        return ''.join(random.choice('01') for _ in range(length))
+    
+    number = generate_binary_number(num_bits)
+    
+    def calculate_twos_complement(binary_str, length):
+        if binary_str == '0' * length:
+            return binary_str  # 2's complement of 0 is still 0
+        # Invert the bits (1's complement)
+        ones_complement = ''.join('1' if bit == '0' else '0' for bit in binary_str)
+        # Add 1 to the 1's complement
         twos_complement = bin(int(ones_complement, 2) + 1)[2:]
-        twos_complement = twos_complement.zfill(len(number))
-        return ones_complement, twos_complement
-
-    ones_complement, correct_answer = calculate_twos_complement(number)
-    options = [correct_answer]
-
+        # Ensure the result is truncated or zero-padded to fit the specified bit length
+        return twos_complement.zfill(length)[-length:]
+    
+    correct_answer = calculate_twos_complement(number, num_bits)
+    
+    options = {correct_answer}
+    
+    # Generate incorrect answers
     while len(options) < 4:
-        invalid_number = ''.join(random.choice('01') for _ in range(bit_length))
-        if invalid_number != correct_answer:
-            options.append(invalid_number)
+        invalid_number = generate_binary_number(num_bits)
+        invalid_twos_complement = calculate_twos_complement(invalid_number, num_bits)
+        if invalid_twos_complement != correct_answer:
+            options.add(invalid_twos_complement)
     
+    options = list(options)
     random.shuffle(options)
     
-    question = f"What is the 2's complement of the {bit_length}-bit binary number {number}?"
-
-    num_expr = sp.sympify(f'0b{number}')
-    ones_expr = sp.sympify(f'0b{ones_complement}')
-    twos_expr = ones_expr + 1
-
+    question = f"What is the 2's complement of the {num_bits}-bit binary number {number}?"
+    explanation = f"The 2's complement of the {num_bits}-bit binary number {number} is {correct_answer}."
     step_by_step_solution = [
-        f"Step 1: Start with the original {bit_length}-bit 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"Step 4: The 2's complement of {number} is {correct_answer}."
+        f"Step 1: Invert the bits (1's complement) of the binary number {number}.",
+        f"Step 2: Add 1 to the result to get the 2's complement.",
+        f"Step 3: Ensure the result is a {num_bits}-bit binary number by truncating or zero-padding if necessary.",
+        f"Step 4: The 2's complement of the {num_bits}-bit binary number {number} is {correct_answer}."
     ]
     
-    explanation = f"The 2's complement of the {bit_length}-bit binary number {number} is {correct_answer}. It is calculated by inverting the bits and adding 1."
-
     return {
         "question": question,
         "options": options,