Given Binary Tuple representing binary representation of a number, convert to integer.
Input : test_tup = (1, 1, 0) Output : 6 Explanation : 4 + 2 = 6.
Input : test_tup = (1, 1, 1) Output : 7 Explanation : 4 + 2 + 1 = 7.
Method #1 : Using join() + list comprehension + int()
In this, we concatenate the binary tuples in string format using join() and str(), then convert to integer by mentioning base as 2.
Python3
# Python3 code to demonstrate working of # Convert Binary tuple to Integer# Using join() + list comprehension + int()# initializing tupletest_tup = (1, 1, 0, 1, 0, 0, 1)# printing original tupleprint("The original tuple is : " + str(test_tup))# using int() with base to get actual numberres = int("".join(str(ele) for ele in test_tup), 2) # printing result print("Decimal number is : " + str(res)) |
The original tuple is : (1, 1, 0, 1, 0, 0, 1) Decimal number is : 105
Method #2: Using bit shift and | operator
In this we perform left bit shift and use or operator to get binary addition and hence compute the result.
Python3
# Python3 code to demonstrate working of# Convert Binary tuple to Integer# Using bit shift and | operator# initializing tupletest_tup = (1, 1, 0, 1, 0, 0, 1)# printing original tupleprint("The original tuple is : " + str(test_tup))res = 0for ele in test_tup: # left bit shift and or operator # for intermediate addition res = (res << 1) | ele# printing resultprint("Decimal number is : " + str(res)) |
The original tuple is : (1, 1, 0, 1, 0, 0, 1) Decimal number is : 105
Time Complexity: O(n)
Auxiliary Space: O(n)
Method #3 : Using list(),map(),join(),int() methods
Python3
# Python3 code to demonstrate working of# Convert Binary tuple to Integer# initializing tupletest_tup = (1, 1, 0, 1, 0, 0, 1)# printing original tupleprint("The original tuple is : " + str(test_tup))# using int() with base to get actual numberx = list(map(str, test_tup))x = "".join(x)res = int(x, 2)# printing resultprint("Decimal number is : " + str(res)) |
The original tuple is : (1, 1, 0, 1, 0, 0, 1) Decimal number is : 105
Method #4: Using for loop
Python3
# Python3 code to demonstrate working of# Convert Binary tuple to Integer# initializing tupletest_tup = (1, 1, 0, 1, 0, 0, 1)# printing original tupleprint("The original tuple is : " + str(test_tup))res = 0j = 0for i in range(len(test_tup), 0, -1): x = 2**j res += x*test_tup[i-1] if(j > len(test_tup)): break j += 1# printing resultprint("Decimal number is : " + str(res)) |
The original tuple is : (1, 1, 0, 1, 0, 0, 1) Decimal number is : 105
Method: Using pow() function
Python3
binary_tuple = (1, 1, 0)result = 0length = len(binary_tuple)for i in range(length): element = binary_tuple[length - i - 1] result = result + element*pow(2, i)print("The output integer is:", result) |
The output integer is: 6
Method#5: Using bit shifting and bitwise operations
Approach:
- Initialize a variable ‘res’ to 0 to store the decimal number representation of the binary tuple.
- Traverse the binary tuple and do the following:
a. Shift ‘res’ one bit to the left.
b. OR ‘res’ with the current bit of the binary tuple. - The result stored in ‘res’ is the decimal number representation of the binary tuple.
Python3
# initializing tupletest_tup = (1, 1, 0, 1, 0, 0, 1)# printing original tupleprint("The original tuple is : " + str(test_tup))# using bit shifting and bitwise operations to get actual numberres = 0for bit in test_tup: res = (res << 1) | bit# printing resultprint("Decimal number is : " + str(res)) |
The original tuple is : (1, 1, 0, 1, 0, 0, 1) Decimal number is : 105
Time Complexity:
The time complexity of this approach is O(n), where n is the length of the binary tuple. This is because the binary tuple is traversed only once.
Auxiliary Space:
The space complexity of this approach is O(1), as we are not using any additional data structures to store the intermediate results. We are using a single variable ‘res’ to store the decimal number representation of the binary tuple.
Method#6: Using Recursive method.
Algorithm:
- Check if the length of the input binary tuple is zero. If it is, return 0.
- If the length of the tuple is not zero, calculate the decimal value of the first element of the tuple by multiplying it with 2 raised to the power of the length of the tuple minus one, and add this value to the result of a recursive call to the same
- function with the rest of the tuple (excluding the first element).
- Return the final result.
Python3
def binary_tuple_to_int(binary_tup): if len(binary_tup) == 0: return 0 else: return binary_tup[0] * 2**(len(binary_tup)-1) + binary_tuple_to_int(binary_tup[1:])# initializing tupletest_tup = (1, 1, 0, 1, 0, 0, 1)# printing original tupleprint("The original tuple is : " + str(test_tup))# calling recursive methodres = binary_tuple_to_int(test_tup)# printing resultprint("Decimal number is : " + str(res)) |
The original tuple is : (1, 1, 0, 1, 0, 0, 1) Decimal number is : 105
The time complexity of this algorithm is O(n), where n is the length of the binary tuple, since we are making a recursive call for each element in the tuple.
The auxiliary space is also O(n), since the function call stack will contain n recursive calls at its maximum depth.
