Convert the following decimal numbers to the indicated bases:

$($a$)7562\mathrm{.}45$ to octal

$($b$)1938\mathrm{.}257$ to hexadecimal

$($c$)175\mathrm{.}175$ to binary

Show the signals of the outputs $F$ and $G($shown below$)$ in the two gates. Use all $16$ possible combinations of the input signals $A,B,C$ and $D$

Draw the logic diagram corresponding to the following Boolean expressions without simplifying them

$($a$)B{C}^{\text{'}}+AB+$ACD

$($b$)(A+B)(C^{\text{'}}D)(A^{\text{'}}+B+D)$

$($c$)(A^{\text{'}}B+A{B}^{\text{'}})(C{D}^{\text{'}}+C^{\text{'}}D)$

Given the following Boolean function:

$F=x{y}^{\text{'}}z+x^{\text{'}}{y}^{\text{'}}{z}^{\text{'}}+w{x}^{\text{'}}y+wx{y}^{\text{'}}+wxy$

$($a$)$ Obtain the truth table of the function

$($b$)$ Draw the logic diagram using the original Boolean expression

$($c$)$ Obtain the truth table of the function from the simplified expression and show that it is the same as the one in part $($a$)$

$($d$)$ Draw the logic diagram from the simplified expression and compare the total number of gates with the diagram of part $($b$)$

$5.$ Name all known drawing with a description of need of named drawing