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 $$f(s) = n$$.

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.

What does the function $$f$$ do?

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:

#### Explainer: The Rigged Bits

By Neeldhara Misra

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