$[6]$ Express multiplication operation using only the specified number of shift and add$/$sub operations:

$x^{**}7,$ using $1$ shift and $1$ Add$/$Sub

$x^{**}(-12),$ using two shifts and $1$ Add$/$Subs

$[8]$ Assuming an $8-$bit machine, is the following expression true or false? Apply the appropriate Casting and explain why it is true or false.

$($a$)-127==127U$

$($b$)-127-1U==127$

$($c$)-1U<mn\; id="EditorElement\_316386">1</mn><mn\; id="EditorElement\_316387">2</mn><mn\; id="EditorElement\_316388">8</mn><mi\; id="EditorElement\_316390">U</mi>$

$($d$)255U=-128$

$[4]$ Derive a minimal expression from the following $k-$map.

$AB$

$\backslash$table$[[,00,01,11,10],[00,1,1,1,1],[01,0,1,1,0],[11,0,1,1,0],[10,0,0,0,1]]$