Can someone help me answer these couple of questions? Any help would be apprecia

Question

Can someone help me answer these couple of questions? Any help would be appreciated!

13. Name three appliances that are candidates for being run by an embedded CPU.

14. At a certain point in time, a transistor on a chip was 0.1 micron in diameter. According

to Moore’s law, how big would a transistor be on next year’s model?

11. A certain computer can be equipped with 1,073,741,824 bytes of memory. Why would

a manufacturer choose such a peculiar number, instead of an easy-to-remember number

like 1,000,000,000?

12. Devise a 7-bit even-parity Hamming code for the digits 0 to 9.

13. Devise a code for the digits 0 to 9 whose Hamming distance is 2.

14. In a Hamming code, some bits are ‘‘wasted’’ in the sense that they are used for checking

and not information. What is the percentage of wasted bits for messages whose

total length (data + check bits) is 2n 1? Evaluate this expression numerically for values

of n from 3 to 10.

Explanation / Answer

Q-12: Devise a 7-bit even-parity Hamming code for the digits 0 to 9?

Even parity means the total number of 1 in the code must be even.Let us suppose the each digit is represented using the 4 bits and 3 redundent bits are added after hamming code generation and maintaing the even parity.So the following table is been developed after devising the hamming code for each digit from 0 to 9.

0

0001111

Q13. Devise a code for the digits 0 to 9 whose Hamming distance is 2.

Hamming distance between two binary codes of n digit is the total number of difference between corresponding digits of the given two binary codes. Hamming distance is represented by d(x,y) where d specifies the disatnce and x,y are the two binary codes.For example if x=0101 and y=1100 then d(x,y)=2 since there are only 2 positions in the given codes at which the digits are different.

This way we can find binary code for digits 0 to 9 which have the hamming disatance 2 .Let us suppose each digit is represented by 4 digit and in d(x,y), x is given digit and y is resultant code for hamming distance 2. so we have as following-

For 0: d(0000,0011)=d(0000,1100)=d(0000,1010)=d(0000,0110)=d(0000,1001)=2 [hence there are multiple codes are possible for a given code to generate a particular hamming distance]

For 1: d(0001,1101)=2

For 2: d(0010,1110)=2

For 3: d(0011,1111)=2

For 4: d(0100,0111)=2

For 5: d(0101,0110)=2

For 6: d(0110,1111)=2

For 7: d(0111,0100)=2

For 8: d(1000,1011)=2

For 9: d(1001,1111)=2

Q11.A certain computer can be equipped with 1,073,741,824 bytes of memory. Why would

a manufacturer choose such a peculiar number, instead of an easy-to-remember number

like 1,000,000,000?

Since the computer memory is built using the flip-flops[basic building blocks of memory used to store one binary bit either 0 or 1] and this flip-flops has only 2 states either on[bit stored in it is 1] or off[bit stored is 0]. To store 1 byte[8 bits] of binary information we will require 8 flip-flops made circuitry and using basic multiplication theory we can store 2^8 different binary codes since each flip-flop is capable of holding 2 bits.

Hence memory in computer is represented using power of 2 due to two bistate flip-flops. Apart form this most of the basic component of computer like decoder/encoder works on the concept of bistate theory.

1KB=1 kilo byte has 2^10 address each has 8 flip-flops=1024 Bytes.

1MB=1 Mega Byte has 2^20 memory address each has 8 flip-flops=1048576 Bytes

And so on......

So memory capacity is represented in the power of two not the power of 10 that is why when we are converting this power of 2 form into byets they seems complex representation of memory as compare to simple power of 10 form.

14. In a Hamming code, some bits are ‘‘wasted’’ in the sense that they are used for checkingand not information. What is the percentage of wasted bits for messages whosetotal length (data + check bits) is 2n 1? Evaluate this expression numerically for valuesof n from 3 to 10.

According to the given situation the calculation of wastage percentage can be given as following for different values of n.

Digit 4 bit code 7 bit hamming code with even parity

0

0000 1 0001 1101001 2 0010 0101010 3 0011 1000011 4 0100 1001100 5 0101 0100101 6 0110 1100110 7 0111

0001111

8 1000 1110000 9 1001 0011001

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