Many computers use one byte (8 bits) of data for each letter of the alphabet. Th

Question

Many computers use one byte (8 bits) of data for each letter of the alphabet. There are 44 million words in the Encyclopedia Britannica. a. What is the bit density (bitslin') of the head of a pin if the entire encyclope- dia is printed on it? Assume the average word is five letters long bA What is the byte density? c. What is the arca of a single bit in nm ? &. A CD ROM has a storage density of 16 megabytes/in. and a DVD hasa storage density of 329 megabytes/in. Is the pinhead better or worse than these two storage media? How much better or worse?

Explanation / Answer

Solution:

Part a. and b.

Suppose the Head of the pin is (1/16)th of an inch in diameter.

The the area is = pi*(1/(2*16))2

= pi*(1/32)2

Given that each word is on an average 5 letters long, and there are 44 million words.

there is a total of  220000000 bytes.

220000000 bytes = 1.76 billion bits ( Since,1 Bytes=8 bits)

therefore there are  1.76 billion bits total over the head of the pin.

The bit density is bits pre unit area,

Bit density = 1.76billion bits/(pi*(1/32)2 bits(inch)-2

approx 574 trillion bits per (inch)2

Byte density is a measure of the quantity of information bytes that can be stored on a given length of track, area of surface, or in a given volume of a computer storage medium.

Byte density is bit density divided by 8

Part c.

inch2 = (2.54cm2) = (25.4e-6nm)2.

So for area divide 574billion by (25.4e-6nm)2

Part d.

Pin Head is better as higher density is more desirable, as it allows greater volumes of data to be stored in the same physical space.

574 trillion bits per inch2 = about 75 trillion bytes per inch2

= 75 terabytes per inch2

here the CD-ROM have storage density only 329 megabytes per inch2.

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