Binary Codes Presentation

Binary codes

by Radhika Saju

Course Outcome

• To state the need for binary codes

• To describe BCD codes, excess-3 code, Gray code

• To describe alpha numeric codes such as ASCII code and EBCDIC

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State the need for binary codes

• Following is the list of advantages that binary code offers.

  • Binary codes are suitable for the computer applications.

  • Binary codes are suitable for the digital communications.

  • Binary codes make the analysis and designing of digital circuits if we use the binary codes.

  • Since only 0 & 1 are being used, implementation becomes easy.

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​Weighted codes: In weighted codes, each digit is assigned a specific weight according to its position. For example, in 8421BCD code, 1001 the weights of 1, 0, 0, 1 (from left to right) are 8, 4, 2 and 1 respectively.

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​8421BCD, 2421BCD are all weighted code

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​Non-weighted codes: The non-weighted codes are not positionally weighted. In other words, each digit position within the number is not assigned a fixed value ( or weight ).

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​Excess-3 and gray code are non-weighted codes.

Multiple Choice

Which is an example of Weighted code

• Gray code

• XS3 code

• Alphaneumeric codwe

• 8421 BCD code

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Sequential codes: In sequential codes, each succeeding ‘code is one binary number greater than its preceding code. This property helps in manipulation of data.

             8421 BCD and Excess-3 are sequential codes.

​Binary Coded Decimal (BCD) code

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• In this code each decimal digit is represented by a 4-bit binary number.

• BCD is a way to express each of the decimal digits with a binary code.

• In the Binary, with four bits we can represent sixteen numbers (0000 to 1111). But in BCD code only first ten of these are used (0000 to 1001). The remaining six code combinations i.e. 1010 to 1111 are invalid in BCD.

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Advantages

• It is very similar to decimal system.

• We need to remember binary equivalent of decimal numbers 0 to 9 only.

Disadvantaged

• The addition and subtraction of BCD have different rules.

• The BCD arithmetic is little more complicated.

• BCD needs more number of bits than binary to represent the decimal number. So BCD is less efficient than binary.

Multiple Choice

Which is an invalid 8421 BCD number

• 1001

• 1000

• 1011

• 0111

Excess-3 code

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The Excess-3 code is also called as XS-3 code. It is non-weighted code used to express decimal numbers. The Excess-3 code words are derived from the 8421 BCD code words adding (0011)₂ or (3)10 to each code word in 8421.

​Gray Code

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It is the non-weighted code and it is not arithmetic codes. That means there are no specific weights assigned to the bit position. It has a very special feature that, only one bit will change each time the decimal number is incremented as shown in fig. As only one bit changes at a time, the gray code is called as a unit distance code. The gray code is a cyclic code. Gray code cannot be used for arithmetic operation.