The basic storage unit of a digital computer is a “bit”. A bit is a storage posi

Question

The basic storage unit of a digital computer is a “bit”. A bit is a storage position that can be designated as either on (1) or off (0) at any time. In converting picture images to a form that can be transmitted electronically, a picture element, called a pixel is used. Each pixel is quantized into gray levels and coded using a binary code. For example, a pixel with four gray levels can be coded using two bits by designating the gray levels by 00, 01, 10, and 11. (a) How many gray levels can be quantized using an eight-bit code? (b) How many bits are necessary to code a pixel quantized to 64 gray levels?

Explanation / Answer

Each bit has possible values : 0 , 1

8-bit code can have 28 posssible values:

First bit has 2 choices (0,1) - 2

Second bit also has 2 choices (0,1) - 2

.....

...n bit also has two choices (0,1) -2

therefore n-bit can have 2n grey levels(choices)

Therefore 8-bit can have 28 = 256 gray level

using an eight-bit code , number of gray levels can be quantized = 256.

(b) Number bits that are necessary to code a pixel quantized to 64 grey levels.

let 'x' be the number of bits that are necessary; to code a pixel quantized to 64 grey levels

then 2x = 64 ; x =6; as 26 = 64

therefore 6 bits that are necessary to code a pixel quantized for 64 grey levels.

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