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The $8$ to $3$ Encoder or Octal to Binary encoder consists of $8$ inputs : $O_{7}$ to $\mathrm{O}_{0}$ and $3$ outputs $: B_{2}, B_{1}$ and $\mathrm{B}_{0}$. Each input line corresponds to each octal digit and three outputs generate corresponding binary code. ( Ex : If input line $\mathrm{O}_{4}$ is set, Output should be $B_{2}=1, B_{1}=0, B_{0}=0$ ). $\mathrm{B}_{2}$ is the Most Significant Bit. Consider following Logical expression for
$$
\begin{aligned}
&B_{2}, B_{1} \text { and } \mathrm{B}_{0}
&B_{2}=O_{7}+O_{6}+O_{5}+O_{4}
&B_{1}=O_{7}+O_{6}+O_{3}+O_{2}
&B_{0}=O_{7}+O_{5}+O_{3}+O_{2}
\end{aligned}
$$
Which of the above Logical Expression(s) is/are CORRECT ?

  1. Only $B_{2}$ is Correct
  2. $B_{1}$ and $B_{2}$ are Correct
  3. $B_{0}$ and $B_{1}$ are Correct
  4. All of them are Correct
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The possible value of  B2  B1  B0    if i/p is applied to 8x3 encoder :-

           if input is O o       0     0      0

          if input is O 1        0     0      1

          if input is O 2        0     1      0

          if input is O 3        0     1     1

          if input is O 4       1     0      0 

          if input is O 5       1     0      1

          If input is O 6       1     1      0

           If input is O 7      1     1      1

 

So, B2==1 if either i/p is applied O4+O5+O6+O7 

      B1==1 If either i/p is applied  O2+O3+O6+O7

      B0==1 If either i/p is applied  O1+O3+O5+O7.

As per given logical expression in question only B2 and B1 is correct. So, answer is B.

Correct me i am wrong.

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