a$)$ Convert the following numbers to decimal system

$[3$M$]$

i$.(1001001\mathrm{.}011{)}_2$

ii$.(1342)8$

iii. $(198{)}_{12}$

b$)$ Perform the subtraction with the following binary numbers using l$\text{'}$s complement

i$.(11010-1101{)}_2$

ii$.(10010-10011{)}_2$

iii. $(11010-10000{)}_2$

$[3$M$]$

c$)$ Implement the $F(a,b,c)={\displaystyle \underset{?}{\overset{?}{}}}(1,2,3,5,7)$ using different gates.

$[4$M$]$

a$)$ Define the universal gates. Implement basic gates using the two universal gates. $[3$M$]$

b$)$ Design the full added and explain with the truth table. $[3$M$]$

c$)F=A(B+CD)+BC\text{'}$ with NAND gates.

a$)$ An $8-$bit register contains the binary value $10011100.$ What is the register value after

an arithmetic shift right and shift left. and state whether there is an overflow $?[4$M$]$

b$)$ Explain the various logical micro$-$operations with the notations. $[3$M$]$

c$)$ Starting from an initial value of $R=11011101,$ determine the sequence of binary values in R after a logical shift$-$left, followed by a circular shift$-$right, followed by a logical shift$-$right and a circular shift$-$left.

$[4$M$]$

a$)$ What is the difference between a direct and an indirect address instruction?

$[3$M$]$

b$)$ Illustrate how many references to memory are needed for such type of instruction to bring an operand into a processor register? $3M$