Weighted and Non Weighted Codes

Get quick hands on Digital Circuits.

1. WEIGHTED AND NON WEIGHTED CODES

2. In weighted code , each digit position has a weight or value. The sum of all digits multiplied by a weight gives a total amount being represented. Bcd or 8421 is a type of weighted code where each digit position is assigned a specific weight.

3. IN NON WEIGHTED CODE THERE IS NO POSITIONAL WEIGHT I.E. EACH POSITION WITHIN THE BINARY NUMBER IS NOT ASSIGNED A PREFIX VALUE. NO SPECIFIC POSITIONS ARE ASSIGNED TO BIT POSITIONS IN NON WEIGHTED CODE. THE NON WEIGHTED CODES ARE (I) GRAY CODE. (II) EXCESS-3 CODE.

4. IT IS COMPOSED OF FOUR BITS REPRESENTING THE DECIMAL DIGITS 0 TO 9. THE 8421 INDICATES THE BINARY WEIGHTS OF THE FOUR BITS ( FOUR POWERS OF 2).

5. BCD ADDITION IS SAME AS BINARY ADDITION CASE 1- IF RESULT IS LESS THAN OR EQUAL TO 9 AND CARRY IS 0 THEN IT IS VALID BCD. CASE 2- IF THE RESULT IS GREATER THEN 9 AND CARRY IS 0, THEN ADD 6 TO THE ANSWER TO GET THE VALID BCD CODE. CASE 3- IF RESULT IS LES THAN OR EQUAL TO 9AND CARRY IS 1, THEN ADD 6 IN FOUR BIT COMBINATION.

6. 9’S COMPLEMENT :- 9’S COMPLEMENT OF A NUMBER CAN BE OBTAINED BY SUBTRACTING IT FROM 9 I.E. IF THE NUMBER IS A 3 DIGIT NUMBER SUBTRACT IT FORM 999 . 10’S COMPLEMENT :- 10’S COMPLEMENT OF A NUMBER CAN BE OBTAINED BY ADDING 1 IN THE RESULT OF THE 9’S COMPLEMENT. PACKED BCD :- THE NUMBERS CORRESPONDING TO DECIMAL NUMNERS BEYOND 9 ARE CALLED PACKED BCD.

7. (1) BCD IS LESS EFFICIENT THAN BINARY. E.G (78) 10 = (0111 1000) BCD = (1001110) 2 BCD ARITHMETIC IS MORE COMPLICATED THAN BINARY ARITHMETIC. ADVANTAGE OF A BCD CODE IS THAT CONVERSION FROm DECIMAL TO BCD OR VICE VERSA IS SIMPLE.

8. IT IS A NON WEIGHTED CODE WHERE EACH NUMBER DIFFERS FROM THE PREVIOUS NUMBER BY A SINGLE BIT.

9. BINARY TO GRAY CONVERSION: (I) THE MSB IN THE GRAY CODE IS SAME AS THE CORRESPONDING BIT IN THE BINARY NUMBER. (II) GOING FROM LEFT TO RIGHT , ADD EACH ADJACENT PAIR OF THE BINARY BIT TO GET THE NEXT GRAY CODE BIT AND DISCARD CARRY. GRAY TO BINARY CONVERSION: ( I) THE MSB IN THE BINARY CODE IS SAME AS THE CORRESPONDING BIT OF THE GRAY CODE. (II) AND EACH BINARY DIGIT GENERATED TO A GRAY DIGIT IN THE NEXT ADJACENT POSITION AND DISCARD CARRY.

10. IT IS A NON WEIGHTED CODE, IT IS A FOUR BIT CODE WHICH IS USED WITH BCD NUMBERS. CONVERSION :- TO CONVERT ANY DECIMAL NUMBER TO ITS EXCESS-3 FORM, ADD 3 TO EACH DECIMAL DIGIT AND CONVER THE SUM TO BCD.