How can this boolean algebra equation be solved?

Question

(7EFEFEFF + A) ^ (A ^ FFFFFFFF) = 81010100 

How can it be solved for the value A? where

• '+' means plus
• '^' is bitwise XOR

EDIT: Forgot to mention. A is a hexadecimal variable

Answer 1

Are you sure the first number ends in $FF$ and not $EF$? I am not sure there is an answer as you have written. I will change it to $EF$ and proceed.

I will give you partial answer and let you work out the rest!

$A\hbox{^}FFFF....$ is bit-wise complement of $A$ which is often denoted as $\hbox{~}A$

Note that the last two nibbles of (something ^ ~A) is $00$. So if we look at the last two nibbles of $A$ and call it $B$ then looking at last two nibbles $$ EF + B = ~B$$ So $B$ should end in $8$ and by the same logic, nibble before the last should be 0 or 8 So $A$ ends in $08$ or $88$.

Working along the same lines we get $A=00000008$ and here are the rest of the calculations: $$ \begin{align} A &=00000008\\ 7EFEFEEF +A &=7EFEFEF7\\ A \hbox{^} FFFFFFFF &= FFFFFFF7\\ (7EFEFEEF +A )\hbox{^}(A\hbox^FFFFFFFF) &=81010100 \end{align} $$