Question: 1. *(a) How many data bits are required to store one of the decimal digits 0 through 9? *(b) How ……

1.

*(a) How many data bits are required to store one of the decimal digits 0 through 9? *(b) How many parity bits are required to detect a single error? (c) Write a single-error detection code using even parity. Underline the parity bits. (d) What is the code distance of your code?

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2.

A set of eight data bits is transmitted with the single-error correction code of Figure 9.25. For each of the received bit patterns below, state whether an error occured. If it did, correct the error.

*(a) 1 0 0 1 1 0 1 0 1 0 0 1

(b) 1 1 0 1 0 0 1 1 0 0 1 0

(c) 0 0 0 0 1 0 1 1 0 1 0 0

(d) 1 0 1 1 0 0 1 0 0 1 0 0

Figure 9.25: FIGURE 9.25 The position of the four parity bits in a single-error-correcting code with eight data bits. 1 2 3 4 5 6 7 8 9 10 11 12

3.

You have a RAID level 4 system with eight data disks and one parity disk. (a) How many disk reads and disk writes must you make to write one data stripe if you do not make use of the old data and parity values? (b)How many disk reads and disk writes must you make to write one data stripe if you do make use of the old data and parity values?

Expert Answer

answers

a) How many data bits are required to store one of the decimal digits 0 through 9?

Ans) 4 bits needed to represent decimal 0-9

Explanation:-

0 –> 0000    1 –> 0001       2–> 0010    3 –>>0011       4 –>0100       5–>0101   

6 –> 0110      7 –> 0111       8 –> 1000    9 –>1001

—————————————————————————————————————–

b) How many parity bits are required to correct a single error?

Ans) 3 bit

Explanation:-

we are using formulae 2r >=d+r+1

where,r=number of parity bit and d=number of data bits

Here, 23 >= 4+3+1

—————————————————————————–

c) Write a single-error correction code using even parity. Underline the parity bits.

   Ans) Conside decimal number 1,

           0001 is the data to be transmitting.

Then we need 3 parity bits for detection(23 >= 4+3+1),

P1 P2   D1 P3 D2 D3 D4

1    0        0     0    0     0     1

Using even parity hamming.

If data change into 0000 while transmitting,then

receiving end it detect and correct by following way,

actual data          100001

CorreptedData   1000000

XOR                       0000001

So, last bit error detected and correct it .

————————————————————————————————————————–

d) What is the code distance of your code?

Ans) 2

Explanation:-

Distance-1=error detection

So,1 bit error=2-1

Eg:-

0001   data

00011 parity added message

00000 changed data

so there is 2 bit change , meand distance=2

———————————————————————————————————————-

16) A set of eight data bits is transmitted with the single-error correction code .Check error occured or

           not

Ans)

a) 1 1 0 1 0 0 1 1 0 0 1 0 –>yes error occured

We transmit following,

11 0 1 1 0 01 0 1 1 0 0

1110 is the transmitting parity bit

but we get 1111 parity bit so correct 1 bit

it will get

1 1 0 1 0 0 1 1 0 0 0 0

——————————————————————————–

b)0 0 0 0 1 0 1 1 0 1 0 0 –>yes error occure

We transmit following,

11 0 1 1 0 01 0 1 1 0 0

1110 is the transmitting parity bit

but we get 0001 parity bit so correct 1 bit

we get

0 0 0 0 1 0 1 1 0 1 1 0

———————————————————————————————————————-

c) 1 0 1 1 0 0 1 0 0 1 0 0 —>error occure

We transmit following,

11 0 1 1 0 01 0 1 1 0 0

1110 is the transmitting parity bit

but we get 0001 parity bit so correct 1 bit

we get,

1 0 1 1 0 0 1 0 1 1 0 0

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