Collectible Stocks and Bonds from North American Railroads             by Terry Cox

A guidebook and catalog of prices
(I neither buy nor sell stocks and bonds)
Understanding Bits  


When buying scanners, you will see them described with with terms like "24-bit color" or "36-bit color." That is simply computer jargon (geek-speak) meant to tell you how accurately the machine will sample color.

Let's dispel the mystery.

What is a bit?

A bit is the smallest unit of digital measurement. You can think of a bit as being like a tiny electronic switch. Each bit can only be switched on or off. There is no in-between.

A single bit cannot do a lot by itself. It can really only indicate one of two possible values such as off or on, 0 or 1, no or yes, black or white, minus or plus, demagnetized or magnetized, etc. By combining bits, you can build larger and larger values that can stand for numbers, letters, sentences, databases and whole libraries. When properly combined, bits can achieve infinite amounts of communication. In fact, bits are the entire backbone of all computing. Here is how you can combine bits to tell you more than simple on and off.

Let's say you want to scan an ordinary stock certificate and you only have one bit at your disposal. Off equals black and on equals white. If you measure an ordinary stock certificate in that manner, you would probably decide that anything more white than black would be called "white." Anything more black than white would be called "black." Your single bit gives you only two choices:

If your certificate is:
you must call it :
0% black to 50% black
"white"
50.01% black to 100% black
"black"

You might not want to, but you would probably say your certificate is "white" because ordinary stock certificates are more white than black.

Obviously, calling a stock certificate "white" conveys little information.

Now, imagine that your equipment is better and allows you to measure your ordinary certificate in smaller increments. Let's say you divide your certificate into tiny squares, 1/100th of an inch on a side. A certificate like the one shown below would contain 968,220 squares.

If you measure the brightness of the whole spectrum at each of the 968,200 points with one bit each, you can portray your certificate with 1-bit accuracy. Once measured, you could then store that information and then use it to display on a monitor.

Your result would look like this. Every bit is either white or black. There are no in-between shades of gray. An image in 1-bit accuracy looks like this.

Now that you've seen a 1-bit representation, you can probably imagine that the next logical step is to describe each sample point with two or more bits.

By using two bits (like two switches), you could measure and display each sample point as black, white, and two shades of gray. Instead of having two possible choices, you now have four:

If your certificate is:
you must call it :
75.01% black to 100% black
"black"
50.01% black to 75% black
"dark gray"
25.01% black to 50% black
"light gray"
0% black to 25% black
"white"

Amazingly, just one extra bit (!) gives a 4x increase in accuracy. Because each sample is measured with two bits instead of one, the file size is double that of the previous image. The image is still manageable small, so why not add even more bits?

Let's say you display a certificate with 4 bits per pixel. You can calculate your possibilities simply by multiplying: 2 x 2 x 2 x 2 = 16. You can see that 4 bits gives you the possibility of measuring and displaying 16 shades of gray. The appropriate jargon would be "4-bit depth." Here is what 4-bit accuracy looks like.

Because so much of the certificate is an in-between shade of gray, we first don't see an equally dramatic improvement over the previous image. However, look closer. See the four cancellation holes at left? Those were "light gray" before, and so ended being quantified the same as much of the rest of the certificate. The cancellation holes were missing from the previous example. Also look at Vanderbilt's coat. We can see some shades of gray that were previously lost in the "dark gray" classification.

If you double your bit-depth once again, from 4 bits to 8 bits, you increase your accuracy of rendering grays even more dramatically. With 8 bits, you can show 256 different shades of gray. (2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256 possible combinations of off/on).

Why stop at 8 bits? After all, 9 bits would give us 512 possible shades of gray and 10 bits would give us 1,024 shades.

It turns out that the young human eye cannot distinguish significantly more than 256 shades of gray. Certainly not 512 shades. Consequently, it does not make much sense to add more bit depth for shades of gray (grayscale in computer jargon) meant to be viewed by humans.

So, how do we measure color?

Measuring gray is simply a matter of measuring brightness and darkness across all of the visible spectrum. If you added a red filter over your certificate, you could measure shades of red using the same equipment. Similarly, you could add green and blue filters and measure shades of green and blue.

It turns out that you can measure almost any color of the visible spectrum simply by measuring the amount of light that passes through calibrated red, green, and blue filters. Scanners and digital cameras are designed to measure reflected colored light directly without the need for actual transparent filters.

Scanners and digital cameras closely measure the amount of red, green, and blue bouncing off an object with nearly the same degree of accuracy that they can measure gray. In geek-speak, each color is called a channel. Using 8 bit bits of sampling accuracy, scanners can distinguish 256 shades of red in the red channel, 256 shades of blue in the blue channel and 256 shades of green in the green channel. (You could add any number of channels, of course, but you immediately surpass human sensory capabilities.)

Add these bits together and you have 24 bits of color being measured at each pixel. (8 bits of red + 8 bits of green + 8 bits of blue). Here is the result of scanning with 24 bits of color capability.

How many different colors can you measure with 24 bits?

Doing the math (2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2x2), we find the theoretical capability of 24 bit sampling is 16,777,216 colors. Needless to say, that is vastly more colors than the best human eye can discern.

But, still, you could add more bits. Right?

Absolutely. In fact, some scanners (but few image manipulation programs) measure 36-bit, even 48-bit color. While the human eye cannot discern such a vast array of color information, engineers can create machines that can. Potential applications for "deep" color information include such things as color matching for paints and dies. Dentistry, for instance, is greatly dependent on matching the colors of implants to existing teeth. Other applications might include accurately discerning micro color differences in surface coatings that have variable translucency, reflectiveness, and glossiness.

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(Last updated July 8, 2011)

 

 

 
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