Flip All Bits in a Width-Limited Integer

EasyPython

Problem

Nissan Motor control software represents some vehicle signals as nonnegative integers stored within a known fixed width. Given an integer value and a bit width width, flip every bit in that width: 0 becomes 1, and 1 becomes 0. Return the resulting value as a decimal integer.

The width is significant because leading zero bits are part of the signal. For example, value = 5 with width = 4 represents 0101, not 101.

Do not convert the value to a binary string. Use bitwise operations and a mask containing width one-bits.

Formal Specification

Implement invert_signal(value, width):

Input: two integers, value and width.
Output: an integer containing the bitwise complement of value within exactly width bits.
The input satisfies 0 <= value < 2**width.

Constraints

1 <= width <= 1,000,000
0 <= value < 2**width
The result must contain no bits above position width - 1

Function Signature

def invert_signal(value, width):

The width is significant because leading zero bits are part of the signal. For example, value = 5 with width = 4 represents 0101, not 101.

Do not convert the value to a binary string. Use bitwise operations and a mask containing width one-bits.

Formal Specification

Implement invert_signal(value, width):

Input: two integers, value and width.
Output: an integer containing the bitwise complement of value within exactly width bits.
The input satisfies 0 <= value < 2**width.