1.15) 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 (bits/in2) of the head of a pin if the entire Encyclopedia is printed on it

provided in the explanation section

Explanation:

the complete questions is given thus:

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 (bits/in2) of the head of a pin if the entire encyclopedia is printed on it? Assume the average word is five letters long. (B). What is the byte density?

(C). What is the area of a single bit in nm2?

(D). A CD-ROM has a storage density of 46 megabytes/in2 and a DVD has a storage density of 329 megabytes/in2. Is the pinhead better or worse than these two storage media? How much better or worse?

ANSWER PROVIDED:

So both quest. a and b will be solved using the same principle.

Let us say we have the Head of the pin as (1/16)th of an inch in diameter.

Then the area is = pi*(1/(2*16))2 = pi*(1/32)2

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

we have a total of  220000000 bytes.

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

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

Note that the bit density is bits per unit area;

since we know that now, let us proceed

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

approx 574 trillion bits per (inch)2

(b). Byte density tells us the measure of the quantity of information bytes that can be stored on a given length of track, area of surface, or even in a given volume of a computer storage medium.

⇒ Byte density is bit density divided by 8

(c). asked to find the area;

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

So to get the area,we will simply divide 574billion by (25.4e-6nm)2

(d). The pin head is WAY better.

what we mean is;

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

= 75 terabytes per inch2

cheers i hope this helped !!!

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