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  ../images/main/bullet_green_ball.gif Binary Codes

Binary codes are codes which are represented in binary system with modification from the original ones. Below we will be seeing the following:

   

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  • Weighted Binary Systems
  • Non Weighted Codes
   

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  ../images/main/bulllet_4dots_orange.gif Weighted Binary Systems

Weighted binary codes are those which obey the positional weighting principles, each position of the number represents a specific weight. The binary counting sequence is an example.

   

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Decimal

8421

2421

5211

Excess-3

0

0000

0000

0000

0011

1

0001

0001

0001

0100

2

0010

0010

0011

0101

3

0011

0011

0101

0110

4

0100

0100

0111

0111

5

0101

1011

1000

1000

6

0110

1100

1010

1001

7

0111

1101

1100

1010

8

1000

1110

1110

1011

9

1001

1111

1111

1100

   

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  ../images/main/bullet_star_pink.gif 8421 Code/BCD Code

The BCD (Binary Coded Decimal) is a straight assignment of the binary equivalent. It is possible to assign weights to the binary bits according to their positions. The weights in the BCD code are 8,4,2,1.

   

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Example: The bit assignment 1001, can be seen by its weights to represent the decimal 9 because:

   

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1x8+0x4+0x2+1x1 = 9

   

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  ../images/main/bullet_star_pink.gif 2421 Code

This is a weighted code, its weights are 2, 4, 2 and 1. A decimal number is represented in 4-bit form and the total four bits weight is 2 + 4 + 2 + 1 = 9. Hence the 2421 code represents the decimal numbers from 0 to 9.

   

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  ../images/main/bullet_star_pink.gif 5211 Code

This is a weighted code, its weights are 5, 2, 1 and 1. A decimal number is represented in 4-bit form and the total four bits weight is 5 + 2 + 1 + 1 = 9. Hence the 5211 code represents the decimal numbers from 0 to 9.

   

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  ../images/main/bullet_star_pink.gif Reflective Code

A code is said to be reflective when code for 9 is complement for the code for 0, and so is for 8 and 1 codes, 7 and 2, 6 and 3, 5 and 4. Codes 2421, 5211, and excess-3 are reflective, whereas the 8421 code is not.

   

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  ../images/main/bullet_star_pink.gif Sequential Codes

A code is said to be sequential when two subsequent codes, seen as numbers in binary representation, differ by one. This greatly aids mathematical manipulation of data. The 8421 and Excess-3 codes are sequential, whereas the 2421 and 5211 codes are not.

   

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  ../images/main/bulllet_4dots_orange.gif Non Weighted Codes

Non weighted codes are codes that are not positionally weighted. That is, each position within the binary number is not assigned a fixed value.

   

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  ../images/main/bullet_star_pink.gif Excess-3 Code

Excess-3 is a non weighted code used to express decimal numbers. The code derives its name from the fact that each binary code is the corresponding 8421 code plus 0011(3).

   

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Example: 1000 of 8421 = 1011 in Excess-3

   

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  ../images/main/bullet_star_pink.gif Gray Code

The gray code belongs to a class of codes called minimum change codes, in which only one bit in the code changes when moving from one code to the next. The Gray code is non-weighted code, as the position of bit does not contain any weight. The gray code is a reflective digital code which has the special property that any two subsequent numbers codes differ by only one bit. This is also called a unit-distance code. In digital Gray code has got a special place.

   

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Decimal Number

Binary Code

Gray Code

0

0000

0000

1

0001

0001

2

0010

0011

3

0011

0010

4

0100

0110

5

0101

0111

6

0110

0101

7

0111

0100

8

1000

1100

9

1001

1101

10

1010

1111

11

1011

1110

12

1100

1010

13

1101

1011

14

1110

1001

15

1111

1000

   

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  ../images/main/4blue_dots_bullets.gif Binary to Gray Conversion
   

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  • Gray Code MSB is binary code MSB.
  • Gray Code MSB-1 is the XOR of binary code MSB and MSB-1.
  • MSB-2 bit of gray code is XOR of MSB-1 and MSB-2 bit of binary code.
  • MSB-N bit of gray code is XOR of MSB-N-1 and MSB-N bit of binary code.
   

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Copyright 1998-2014

Deepak Kumar Tala - All rights reserved

Do you have any Comment? mail me at:deepak@asic-world.com