Foundation of Switching Theory and Logic Design: (As Per by Arun Kumar Singh

By Arun Kumar Singh

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However, in both the cases the original codeword can not be found. If there is even combination of errors (means some bits are changed but parity remains same) it remains undetected. Longitudinal Redundancy Check (LRC) In LRC, a block of bits is organised in rows and columns (table). For example, a block of 16 bits can be organised in two rows and eight columns as shown in Fig. 14. We then calcualte the parity bit (even parity/odd parity, here we are using even parity) for each column and create a new row of 8 bits, which are the parity bits for the whole block.

We have already discussed XS3 code. Gray code (Unit Distance code or Reflective code) There are applications in which it is desirable to represent numerical as well as other information with a code that changes in only one bit position from one code word to the next adjacent word. This class of code is called a unit distance code (UDC). These are sometimes also called as ‘cyclic’, ‘reflective’ or ‘gray’ code. These codes finds great applications in Boolean function minimization using Karnaugh map.

Addition and Carry (CY) Add the two numbers in the step 3 and check whether or not carry generated from MSB due to addition. (Same as (r – 1)’s complement). Mu = 1025, Su = 9950 → Du= 10975 ↓ CY Ms = 9630, Ss = 5688 → Ds = 15318 ↓ CY Step 5. Process the Carry (CY) If there is carry from MSB in step 4 then simply discard it. In step 4, we got CY = 1, Du = 0975 also CY = 1, Ds = 5318. After discarding the carry we get, Du = 0975 and Ds = 5318. Step 6. Result Manipulation The way result is manipulated is different for signed and unsigned arithmetic.

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