CIS3355: Business Data Structures
Fall, 2008
 

How many bits do we need to group together and why??

Actually, the real question should be:

What information do we need to represent?

As we previously saw, once we know how many pieces of information we need to represent, we can readily determine the number of bits we need:

I = Bⁿ

Naturally, we would like to represent all available infomation. However, if the amount of information available is infinite (maybe), then we would need an infinite number of bits (obviously, that is impossible).

For the early computer architects, this issue was extremely troublesome. The materials needed to build and control the "bits" was very expensive (the core memory donuts were often coated in gold, as was the wiring) as was the labor needed (for early computers, all the wiring was strung by hand). Keeping the number of bits grouped together at a minimum was a necessity.

So, what they did decide on?

Each group of computer manufacturers came up with their own schemes, but there were some commonly shared opinions. They wanted to be able to represent:

If we total up the symbols above, we come-up with (about) 112 symbols that we would like to represent.

We know that we will need 7 bits to represent 112 symbols.

How do we know that??

Because given 6 bits, we can only represent 2⁶ = 64 symbols (not enough) whereas with 7 bits we can represent 2⁷ = 128 symbols(which will do it)

I Don't believe that at all!!!
I happen to know that bits are grouped together in units of 8 -- as a byte!!

That is true. However, the early sharacter set consisted of 128 characters (using 7 bits). In fact, the standard ASCII character set (which we will discuss later) still consists of 128 characters.

Then why is a byte 8-bits??

We will discuss that in the next tutorial. However, it has to do with trying to catch transmission errors.

But if 128 characters were available, and they only needed about 112, what happened to the remaining combinations??

They were used. There was no shortages of symbols that architects wanted to represent.

Some good references include:

1.   How Bits and Bytes Work
2.   Bits and Bytes: An Explanation
3.   Character encoding (Wikipedia)

At this point in time, you should be able to Answer the following questions:

1. Why was determining how many bits to group together an issue for early computer architects?
   
   For early computers, the materials needed to build and control the "bits" was very expensive (the core memory donuts were often coated in gold, as was the wiring) as was the labor needed (for early computers, all the wiring was strung by hand). Keeping the number of bits grouped together at a minimum was a necessity.
    
2. Approximately how many bits did early architects feel they needed to group together and why?
   
   There were certain symbols that the architects felt they needed to represent, such as the alphabet, the digits, some special characters, and some computer-operation related symbols. They came up with about 100 symbols that they felt were necessary, meaning they needed 7 bits.
    
3. Early architects had to keep the set of symbols they needed to represent to a minimum. Why?
   
   a.  The computer could only operate at a fast rate if the character set used was very small
   b.   The computer was limited by the number of symbols it could represent
   c.   A large character set would be very difficult to maintain
   d.   The costs of building a computer were very high
   e.   Computer architects are a bizzare lot
   
   Answer: d
    
4. Suppose I had 9 bits I could group together to form a character set. How many characters could I have?
   
   a.  9
   b.   81
   c.   6
   d.   128
   e.   512
   
   Answer: e
    
5. How many bits would I need to represent all states in the United States?
   
   a.  4
   b.   5
   c.   6
   d.   7
   e.   50
   
   Answer: c

   

   This page was last updated on 01/07/05