Assignment $2$

QUESTION $1[40]$

$1\mathrm{.}1$ Convert Binary $1100\mathrm{.}11$ to Decimal. $(6)$

$1\mathrm{.}2$ Convert $7538$ to Hexadecimal. $(6)$

$1\mathrm{.}3$ Using Boolean algebra techniques, simplify the following expression. $(6)$

AB$($A$+$B$)($B$+$B$)+$AB$+$BA$$

$1\mathrm{.}4$ Determine the $2$s complement of $1111001(3)$

$1\mathrm{.}5$ Perform the following additions:

$($a$)2478+7358(4)$

$($b$)1111+1101(4)$

$($c$)8$AB$16+$ B$7816(4)$

$1\mathrm{.}6$ Write the expression in sigma notation:

X$()=$ ABC$$D$+$ AB$$CD $+$ A$$BCD$+$ A$$B$$CD$+$ AB$$C$$D$(5)$

$1\mathrm{.}7$ What is the output of a NAND gate when two inputs are HIGH? $(2)$

QUESTION $2[30]$

$2\mathrm{.}1$ Simplify the expression

W$$ X Y$$ Z$+$ W X Y$$ Z $+$ W X Y$$ Z$+$ W X$$ Y$$ Z $+$ W$$ X$$ Y Z $+$ W$$ X Y Z $+$ W X Y Z $+$ W X Y Z$$

using a Karnaugh map. $(15)$

Please note: use WX in the rows and YZ in the columns

$2\mathrm{.}2$ Write the expanded forms of the terms in the given expression: $(5)$

F $($ABCD$)=$ AC$+$A B C D

$2\mathrm{.}3$ Implement the logic circuit for the expression

F$($WXY$)=($W$+$ X$+$Y$)($W X$+$ Y $$

$)+$ W$$ X Y$.$ Please note: Do not simplify the expression. $(8)$

$2$ ICT$2632$

$2\mathrm{.}4$ Draw the truth table of a $2-$input NOR gate. $(2)$

Question $3.[30]$

$3\mathrm{.}1($a$)$ Convert the given Boolean expression to standard SOP $($Sum of Products$)$ form. $(8)$

X$($ABC$)=$AB$$C$+$A $$C$+$ABCD$+$ BCD

$($b$)$ Write the Boolean expression for the following Logic circuit: $(2)$

$3\mathrm{.}2($a$)$ Discuss the Positive edge triggered J$-$K flip flop and also provide its logic circuit. $(8)$

$($b$)$ Draw the truth table of the Positive edge triggered J$-$K flip flop. $(4)$

$3\mathrm{.}3$ Answer the following two questions:

$($a$)$ Apply Demorgan's theorems to the expression: X $=($A$+$ B$)($AC $$

$)(4)$

$($b$)$ Prove that $($A $+$ BC$)$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$+($AB $$

$)=$ AB$(4)$

TOTAL $[100$ Marks$]$

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UNISA $2024$