The Basics Of Bits (Part II)
In the binary number system, the bit position gains more value (magnitude) as we move to the left (starting from the rightmost bit).
The right most bit is the first bit. Also called the least significant bit (LS
, this holds the value of 0 or 1, second bit holds the value of 0 or 2, the third bit holds the value of 0 or 4, until the last bit, the most significant bit (MS. The MSB can be interpreted two ways:
- As unsigned char this holds a value of 0 or 128.
- As signed char this holds the sign (see figure above). Because the MSB is half the possible range of the bits before it- the range of values that can be represented by the unsigned char is now limited to between -128 to 127.
The value of each bit position adheres to the formula:
| Bit Position | To The Power Of | Binary Value |
|---|---|---|
| 1 (LS |
o or 10 | o or 1 |
| 2 | o or 21 | 0 or 2 |
| 3 | o or 22 | 0 or 4 |
| 4 | o or 23 | 0 or 8 |
| 5 | o or 24 | 0 or 16 |
| 6 | o or 25 | 0 or 32 |
| 7 | o or 26 | 0 or 64 |
| 8 (MSB if unsigned) | o or 27 | 0 or 128 |
| 8 (MSB if signed) | 0 or 10 | 1 or -1 |
Therefore a value of 201 with a binary representation of 11001001 because:
10 + 0 + 0 + 23 + 0 + 0 + 26 + 27
= 1 + 0 + 0 + 8 + 0 + 0 + 64 + 128
= 201
And a value of 247 with a binary representation of 1111 0111 is:
10 + 21 + 22 + 0 + 24 + 25 + 26 + 27
= 1 + 2 + 4 + 0 + 16 + 32 + 64 + 128
= 247
Finally, here’s how we get 255 as the maximum (when all bits are 1)
10 + 21 + 22 + 23 + 24 + 25 + 26 + 27
= 1 + 2 + 4 + 0 + 16 + 32 + 64 + 128
= 255
8 bit numbers are not used in modern day computing because the numbers they can represent are too small for any practical use. We only use this 8 bit data type for one case - character representation (you’d read more on this later).
For numerical purposes we use 32 bit integers on 64 bit computers, and 16 bit integer on 32 bit computers.
| CPU Architecture | Range For Signed | Range For Unsigned |
|---|---|---|
| 32 bit computers (16 bits integers, 2 bytes) | -32,768 to 32,767 | 0 to 65,535 |
| 64 bit computers (32 bits integer, 4 bytes) | -2,147,483,648 to 2,147,483,647 | 0 to 4,294,967,295 |
By now you’d realise what the effects of bit rot can be for the more complex data types, as a flip at the 16th position or 30th position is far more significant than a flip at the 8th position or lower.
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4 comments
Comment from: Frank Collins Visitor
Comment from: Agent Kith Member
It does a four-weekly scrub which detects and corrects bit rot on the whole file system. While bit rot isn’t a problem for me, it never will be.+1. FreeNAS for the win.
Comment from: Agent Kith Member
Maybe it’s Cosmic Rays: https://science.slashdot.org/story/17/02/19/2330251/serious-computer-glitches-can-be-caused-by-cosmic-rays
A "single-event upset" was also blamed for an electronic voting error in Schaerbeekm, Belgium, back in 2003. A bit flip in the electronic voting machine added 4,096 extra votes to one candidate. The issue was noticed only because the machine gave the candidate more votes than were possible. "This is a really big problem, but it is mostly invisible to the public," said Bharat Bhuva. Bhuva is a member of Vanderbilt University’s Radiation Effects Research Group, established in 1987 to study the effects of radiation on electronic systems.
Comment from: Agent Kith Member
Here is an interesting YouTube video about bit flipping.
I don’t believe bit rot is a problem and the Red Book standard copes with missing bits, to a point.
I store all of my music (FLAC, level 8 compression) on a NAS, using FreeNAS. It does a four-weekly scrub which detects and corrects bit rot on the whole file system. While bit rot isn’t a problem for me, it never will be.