The document discusses octal encoding. It explains that octal uses base-8 numerals from 0-7 and can be made from binary by grouping bits into threes. An octal to binary encoder has eight input lines for each octal digit and three output lines to generate the corresponding binary code. Only one input should be active at a time. The encoder can be implemented using OR gates based on output equations. There are issues when all inputs are zero or just the zero input is active.

1. OCTAL ENCODING
C.Rajeswari
I MSc (IT)

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. 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. 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. 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. 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. 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. OCTAL ENCODING(0 T0 7)
 To convert any integer to an octal string, go on diving the
integer by 8
For example:

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. 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. SUMMARY
 Encoders can be used to generate a coded output from s
singular active numeric input line.

12. T
H
A
N
K
I
N
G
Y
O
U