Updates

modules/number_system/grouping_techniques.py

@@ -1,41 +1,81 @@
-# modules/grouping_techniques.py
+# modules/number_system/grouping_techniques.py
 
 title = "Grouping Techniques for Conversion"
-description = "This module focuses on grouping techniques for conversion between bases such as binary and hexadecimal."
+description = "This module focuses on grouping techniques for conversion between bases such as binary, octal, and hexadecimal."
 
 def generate_question():
     import random
 
+    # Choose a random base to convert from, either 2, 8, or 16
     from_base = random.choice([2, 8, 16])
-    to_base = 8 if from_base == 2 else 2
-    number = ''.join(random.choice('01') for _ in range(8))
+    to_base = 8 if from_base == 2 else 2 if from_base == 8 else 2
+    number = ''
+
+    if from_base == 2:
+        # Generate a random binary number, optionally with a fractional part
+        number = ''.join(random.choice('01') for _ in range(random.randint(4, 8)))
+        if random.choice([True, False]):
+            number += '.' + ''.join(random.choice('01') for _ in range(random.randint(1, 4)))
+    elif from_base == 8:
+        # Generate a random octal number, optionally with a fractional part
+        number = ''.join(random.choice('01234567') for _ in range(random.randint(2, 4)))
+        if random.choice([True, False]):
+            number += '.' + ''.join(random.choice('01234567') for _ in range(random.randint(1, 3)))
+    elif from_base == 16:
+        # Generate a random hexadecimal number, optionally with a fractional part
+        number = ''.join(random.choice('0123456789ABCDEF') for _ in range(random.randint(2, 4)))
+        if random.choice([True, False]):
+            number += '.' + ''.join(random.choice('0123456789ABCDEF') for _ in range(random.randint(1, 3)))
 
     def group_conversion(number, from_base, to_base):
-        # Group the binary digits for conversion
         if from_base == 2 and to_base == 8:
-            return oct(int(number, 2))[2:]
+            # Convert binary to octal
+            integer_part, *fraction_part = number.split('.')
+            integer_result = oct(int(integer_part, 2))[2:]
+            if fraction_part:
+                fraction_result = ''.join([oct(int(f'{fraction_part[0][i:i+3]:0<3}', 2))[2:] for i in range(0, len(fraction_part[0]), 3)])
+                return f"{integer_result}.{fraction_result}"
+            return integer_result
         elif from_base == 2 and to_base == 16:
-            return hex(int(number, 2))[2:].upper()
+            # Convert binary to hexadecimal
+            integer_part, *fraction_part = number.split('.')
+            integer_result = hex(int(integer_part, 2))[2:].upper()
+            if fraction_part:
+                fraction_result = ''.join([hex(int(f'{fraction_part[0][i:i+4]:0<4}', 2))[2:].upper() for i in range(0, len(fraction_part[0]), 4)])
+                return f"{integer_result}.{fraction_result}"
+            return integer_result
         elif from_base == 8 and to_base == 2:
-            return bin(int(number, 8))[2:]
+            # Convert octal to binary
+            integer_part, *fraction_part = number.split('.')
+            integer_result = bin(int(integer_part, 8))[2:]
+            if fraction_part:
+                fraction_result = ''.join([bin(int(digit, 8))[2:].zfill(3) for digit in fraction_part[0]])
+                return f"{integer_result}.{fraction_result}"
+            return integer_result
         elif from_base == 16 and to_base == 2:
-            return bin(int(number, 16))[2:]
+            # Convert hexadecimal to binary
+            integer_part, *fraction_part = number.split('.')
+            integer_result = bin(int(integer_part, 16))[2:]
+            if fraction_part:
+                fraction_result = ''.join([bin(int(digit, 16))[2:].zfill(4) for digit in fraction_part[0]])
+                return f"{integer_result}.{fraction_result}"
+            return integer_result
 
     correct_answer = group_conversion(number, from_base, to_base)
-    options = [correct_answer]
+    options = {correct_answer}
 
-    # Generate incorrect answers
+    # Generate incorrect answers ensuring they are unique
     while len(options) < 4:
-        invalid_number = ''.join(random.choice('01234567') for _ in range(4))
-        if invalid_number != correct_answer:
-            options.append(invalid_number)
-    
+        invalid_number = group_conversion(''.join(random.choice('0123456789ABCDEF') for _ in range(len(correct_answer))), from_base, to_base)
+        options.add(invalid_number)
+
+    options = list(options)
     random.shuffle(options)
     
-    question = f"Convert the binary number {number} from base {from_base} to base {to_base} using grouping technique."
-    explanation = f"The number {number} in base {from_base} is {correct_answer} in base {to_base} using grouping technique."
+    question = f"Convert the number {number} from base {from_base} to base {to_base} using grouping technique."
+    explanation = f"The number {number} in base {from_base} is {correct_answer} in base {to_base} using the grouping technique."
     step_by_step_solution = [
-        "Step 1: Group the binary digits in sets of 3 (for base 8) or 4 (for base 16).",
+        "Step 1: Group the digits of the number according to the conversion rules.",
         "Step 2: Convert each group to the corresponding digit in the target base.",
         "Step 3: Combine the digits to form the final answer."
     ]