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# Octal encoding

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Octal to binary encoder
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# Octal encoding

octal encoding

octal encoding

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### Octal encoding

1. 1. OCTAL ENCODING C.Rajeswari I MSc (IT)
2. 2. INTRODUCING OCTAL  The octal numeral system, or oct for short, is the base-8 number system, and uses the digits 0 to 7. Octal numerals can be made from binary numerals by grouping consecutive binary digits into groups of three (starting from the right).  After 7 the next placeholder to this right begins with a “1”
3. 3. ENCODER  An encode is a digit circuit that performs the inverse operation of a decoder. An encoder has 2n(or less)input lines and output lines, An encoder is the octal-to-binary encoder.  It has eight inputs one for each of the octal digits, and three outputs that generate the corresponding binary umbers.
4. 4. OCTAL TO BINARY ENCODER  An octal to binary encoder consist of eight input lines and three output lines. Each input corresponds to each octal digit and three output generate corresponding binary code.  In encoders, it is to be assumed that only one input is active or has a value 1 at any given time otherwise the circuit has no meaning.
5. 5. CONTINUE…  From the above table, the output Q₂ becomes 1 if any of the digits D₄ or D₅ or D₆ or D₇ is one.
6. 6. CONTINUE... Q₂=D₄+D₅+D₆+D₇ Q₁=D₂+D₃+D₆+D₇ and Q₀=D₁+D₃+D₅+D₇  Also do does not exist in any of the expressions so it is considered as don’t care, from the above expressions, we can implement the octal to binary encoding using srt of OR gates.
7. 7. CONTINUE…  There is ambiguity in the octal to binary encoder that when all the inputs are zero, an output with all 0’s is generated.  Also ,when D₀ is 1, the output generated is zero.  This is a major problem in this type of encoder, this can be resolved by specifying the condition the one of the input are active with an additional output
8. 8. OCTAL ENCODING(0 T0 7)  To convert any integer to an octal string, go on diving the integer by 8 For example:
9. 9. CONTINUE….  For the octal code, we can get the equivalent integer by encoding by decoding.  The integer value for the octal code 1036 is 542.
10. 10. CONTINUE….  A four-bit octal string can represent the integers from 0 to 4095 and hence,(0000 0000) and (7777 7777) would represent the points for X₁ and X₂ as (X₁ᴸ,X₂ᴸ); (X₁ᵁ,X₂ᵁ) respectively.  The decoded value of a binary substring Sᵢ is calculated as k=nᵢ-1 ∑ 8ᴷsĸ k=0  And hence, the obtainable accuracy in the variable approximation is (Xᵢᵁ-Xᵢᴸ)/8ⁿⁱ.
11. 11. SUMMARY  Encoders can be used to generate a coded output from s singular active numeric input line.
12. 12. T H A N K I N G Y O U