Sensors

[BMAD]

You have two 3-bit sensors, A and B, that measure the same thing, whatever it is -- temperature of the room, radioactivity levels, whatever. Both sensors are hooked up to the same CPU, which takes in the sensor readings. You know that the sensors are designed so that their readings can be off by at most one bit. We claim that if B knows that A has sent the CPU a 3-bit sequence, then B only needs to send 2 bits, and the CPU will be able to reconstruct B's 3-bit measurement, thereby conserving bandwidth. How is this so?

[bonanova]

B knows A's 3-bit sequence was sent. Does B also know what it is?

[BMAD]

Not necessary for B to know

[harey]

I made a lookup table for the processor.

1st line: measurements by A

1st column: measurements by B

x difference only one bit

. difference more than one bit

0 1 2 3 4 5 6 7

0 x x x . x . . .

1 x x . x . x . .

2 x . x x . . x .

3 . x x x . . . x

4 x . . . x x x .

5 . x . . x x . x

6 . . x . x . x x

7 . . . x . x x x

Observe the horizontal symmetry: B sends (7-measurement)

It makes me think of Grey code...

Sorry I cannot hide it. Maybe because of the font?

Edit: Definitely, I have a problem with the editor.

Edited December 5, 2013 by bonanova
Per request canged table font to courier

[harey]

Correction:

B sends:

- if(measurement<4) measurement else 7-measurement.

P.S. It would not be bad if the table in my previous post magically appeared in a fixed font.

Edited December 5, 2013 by harey

[harey]

Prayer to bona alma:

- correct the post 4 with the correction from the post 5

- delete in the post 4 remarks that are not necessary anymore

- delete the post 5

- delete this post

...and pray with me that bmad concedes it is the Best Answer