Updates

modules/number_system/negative_binary.py

@@ -1,68 +1,61 @@
-# modules/number_system/negative_binary.py
+import random
 
 title = "Negative Binary Numbers"
 description = "This module covers negative binary numbers and their representation."
 
 def generate_question():
-    import random
-
-    # Choose a random bit length between 2 and 8 bits, inclusive
-    bit_length = random.randint(2, 8)
-
-    # Generate a random binary number of the selected bit length
-    number = ''.join(random.choice('01') for _ in range(bit_length))
-
-    def calculate_negative_binary(number):
-        # Example logic: return the 2's complement of the number as its negative representation
-        return bin(int(number, 2) * -1)[3:].zfill(len(number))
-
-    def calculate_decimal_value(number):
-        # Convert the binary number to its decimal value (considering it unsigned)
-        return int(number, 2)
-
-    correct_answer = calculate_negative_binary(number)
-    options = [correct_answer]
-
+    bit_lengths = [2, 3, 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_negative_binary(binary_str):
+        # Interpret the binary string as a signed number
+        if binary_str[0] == '1':
+            # Two's complement
+            ones_complement = ''.join('1' if bit == '0' else '0' for bit in binary_str)
+            twos_complement = bin(int(ones_complement, 2) + 1)[2:].zfill(len(binary_str))
+            decimal_value = -int(twos_complement, 2)
+        else:
+            decimal_value = int(binary_str, 2)
+        
+        return decimal_value
+    
+    def decimal_to_binary(value, length):
+        # Convert a decimal number to binary with a given length
+        if value < 0:
+            value = (1 << length) + value
+        return bin(value)[2:].zfill(length)
+    
+    correct_decimal = calculate_negative_binary(number)
+    correct_binary = decimal_to_binary(correct_decimal, num_bits)
+    
+    options = [correct_decimal]
+    
     # 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)
+        random_decimal = random.randint(-2**(num_bits-1), 2**(num_bits-1)-1)
+        if random_decimal != correct_decimal:
+            options.append(random_decimal)
     
     random.shuffle(options)
     
-    question_type = random.choice(["negative_binary", "decimal_value"])
-    
-    if question_type == "negative_binary":
-        question = f"What is the negative representation of the {bit_length}-bit binary number {number}?"
-        explanation = f"The negative binary representation of the {bit_length}-bit binary number {number} is {correct_answer}."
-        step_by_step_solution = [
-            f"Step 1: Convert the {bit_length}-bit binary number to its 2's complement.",
-            f"Step 2: The result is the negative binary representation."
-        ]
-    else:
-        decimal_value = calculate_decimal_value(number)
-        question = f"What is the decimal value of the {bit_length}-bit binary number {number}?"
-        explanation = f"The decimal value of the {bit_length}-bit binary number {number} is {decimal_value}."
-        step_by_step_solution = [
-            f"Step 1: Convert each bit of the binary number {number} to its decimal equivalent.",
-            f"Step 2: Sum the values considering their place values."
-        ]
-        correct_answer = str(decimal_value)
-        options = [correct_answer]
-
-        # Generate incorrect decimal answers
-        while len(options) < 4:
-            invalid_decimal = str(random.randint(0, 2 ** bit_length - 1))
-            if invalid_decimal != correct_answer:
-                options.append(invalid_decimal)
-        
-        random.shuffle(options)
+    question = f"What is the decimal value of the signed {num_bits}-bit binary number {number}?"
+    explanation = f"The decimal value of the signed {num_bits}-bit binary number {number} is {correct_decimal}."
+    step_by_step_solution = [
+        f"Step 1: Identify if the binary number is positive or negative. The leftmost bit indicates the sign.",
+        f"Step 2: If the leftmost bit is '1', calculate the two's complement to find the magnitude of the negative number.",
+        f"Step 3: Convert the binary number to decimal considering its sign.",
+        f"Step 4: The decimal value of the signed {num_bits}-bit binary number {number} is {correct_decimal}."
+    ]
     
     return {
         "question": question,
         "options": options,
-        "correct_answer": correct_answer,
+        "correct_answer": correct_decimal,
         "explanation": explanation,
         "step_by_step_solution": step_by_step_solution
     }