I have a function \(f\) that takes a 16-bit string as input & produces a number between 0 and 15 as output.

You give me a string \(s \in \{0,1\}^{16}\) and a number \(n \in \{0,...,15\}\).

It will turn out that \(f(t) = n\).

I will flip one bit in \(s\) to get \(t\).

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

\(f(\)

\() = 12.\)

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f\) can be thought of as writing out four bits.

\(f(\)

\() = 7.\)

WANT:

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f(\)

\() = 7.\)

WANT:

\(f\) current:

\(f\) desired:

Think of the bit string of length 16 as being written out in a \(4 \times 4\) grid.

\(f(\)

\() = 7.\)

WANT:

\(f\) current:

\(f\) desired: