You are given the following code table:

$A=110100$

$B=111111$

$C=000111$

$D=001100$

$E=010010$

$F=011001$

$G=100001$

$H=101010$

$5$

$3+5=8$

$($a$)$ Prove that you will be able to correct any single bit error.

$($b$)$ Correctly decode: $110111010000110100001111101010.$