terminology - What do the measurements for colour depth mean?

Colour depth is often referred to as being X bits. What does this mean and how does it effect a photograph? What scale is used, i.e. is it linear, exponential, logarithmic, etc.?

Answer

What is a bit?

Computers store values as binary numbers. Each digit of a binary number is called a bit. 2^N, where N is the number of bits is the maximum number of things that binary number can represent.

Example Please

A black and white image (no gray here, just black and white) can be represented with a color depth of 1 bit. 2^1 = 2. Those two colors are black and white.

Back on older mac computers you could set the color depth: 16 colors, 256 colors, thousands of colors, millions of colors. These options correspond to different bit depth values: 4, 8, 16, and 24 bits. Bit depth on computer monitors always refers to the sum of the red, green, and blue pixels bit depth. If the sum is not divisible by 3, then usually green gets the extra bit since your eye is most sensitive to green.

What are some real world numbers?

Nikon d7000: 14bits per pixel.

Most computer monitors display color with 8 bits per color for a total of 24 bits per pixel.

Scale

Image sensors are linear, which means the half the values represent the brightest stop of light, then the next quarter the next stop and so forth. This means that dark values quickly get compressed into a small number of possible values. The higher the bit depth the better quality dark pixels.

How does it affect a photograph?

More bits means more data. That can't be faked. More bits may also mean more quality to work with when processing the images.

Higher values are not always better though. Designing ADC (analog digital converters) with high bit depth is very difficult. This is because the noise level of the converter must be below (V)/2^N where V is the input signal's voltage and N is the bit depth. This voltage, V/2^N is called the least significant bit voltage (often called 'one LSB'). It is the voltage that each bit represents. If the noise level is greater than one LSB the LSB is not storing useful data and should be removed.

Example: A 5 Volt signal is being digitized by a 10 bit ADC. Under what voltage should noise be kept?

Using the equation for LSB voltage: 5/(2^10) = (5/1024)V, 4.88mV.