$8$ Convert the following $8$ bit binary to two's complement signed integer.

$10000100$

$00100000$

$11111101$

$10001000$

$[4]$ Convert two's complement signed integer to $6-$bit binary.

$-1$

$-26$

$[4]$ Conversion of two's complement to unsigned integer $($Assume bit width is $5),$ Express the answer as a decimal number.

$T2U(-7)$

$T2U(12)$

$[4]$ Conversion of unsigned to two's complement integer $($Assume bit width is $8),$ Express the answer as a decimal number.

$U2T(130)$

$U2T(254)$

$[6]$ 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$)-1U<mn\; id="EditorElement\_347250">1</mn><mn\; id="EditorElement\_347251">2</mn><mn\; id="EditorElement\_347252">8</mn><mi\; id="EditorElement\_347254">U</mi>$

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

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

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