Develop an sec (single error correction) code for a 16-bit data word. generate the code for the data word 0101000000111001. show that the code will correctly identify an error in data bit 4.

The code is given as = 010100000001101000101

Explanation:

The steps take is shown below,

The SEC code is used to ascertain where errors had occurred. Such as the occurrence of errors in data bits.

The inequality given is: 2^k - 1 > = M + K

Where M is = 16

For the arrangement of the data bits and checking of the bits, the following steps is taken below

Bit position Number Check bits Data Bits

21 10101

20 10100

The bits is therefore checked in a way up to the bit position 1

Therefore, the code is then written as follows: 010100000001101000101

010100000001101000101

Explanation:

When an error occurs in data bits, the SEC code is used to determine where the error took place. 5 check-bits are needed to generate SEC code for 16-bits data word. The check bits are:

C16=0, C8=0, C4=0, C2=0, C1=1

Therefore the SEC code is 010100000001101000101