Problem

Given a string b representing a binary number (digits 0 and 1 only), return its decimal value as an integer. The string may be long enough that you must be careful about overflow; a follow-up asks for the value modulo 10^9 + 7, and another asks to solve it without using built-in base conversion.

Input / Output

• Input: binary string b.
• Output: integer (or integer mod 10^9+7 for the long version).

Examples

b	Output
"101"	5
"1111"	15
"0"	0
"100000"	32

Constraints

• 1 <= b.length <= 10^5
• b has no leading +/-; leading zeros are allowed.

Approach

Horner's method (left to right). Maintain value = 0; for each bit d, set value = value * 2 + d. Each step shifts the accumulated value one binary place left and adds the new bit. This is O(n) with a single pass and no need to know the length up front. Using bit operations: value = (value << 1) | d.

Right to left with powers. Walk from the last character, adding d * 2^i for position i. Equivalent but needs a running power.

Overflow. A 64-bit integer holds at most 63 bits, so for long strings either use arbitrary-precision integers (Python) or reduce modulo M at each step: value = (value * 2 + d) % M. The modular version is what appears in contest settings.

Validation. Reject characters other than 0/1 if the input is untrusted.

Complexity

• Time: O(n)
• Space: O(1)

Reference solution (Python)

def binary_to_decimal(b: str) -> int:
    value = 0
    for c in b:
        value = (value << 1) | (ord(c) - 48)
    return value

def binary_to_decimal_mod(b: str, M: int = 10**9 + 7) -> int:
    value = 0
    for c in b:
        value = (value * 2 + (ord(c) - 48)) % M
    return value

Test cases

Input	Expected
"101"	5
"1111"	15
"0"	0
binary_to_decimal_mod("1"*40)	(2**40-1) % (10**9+7) = 511620082