a$)$ Find the $2$s complement of decimal $(538)10$ and also express $(538)10$ in BCD code.

$(3$M$)($BL$-2)$

b$)$ You have studied the significance of the four types of positional number systems in this course. If an equation $($assumed to be correct$)$ is given as$,($A$80)$a $=(5200)$b$.$

Describe in a systematic way, how can you find the values of $$a$,$ and $$b$$ above, just by observing these two numbers, provided that above numbers are either binary, or octal, or decimal, or hexadecimal numbers. $(3$M$)($BL$-3)$

c$)$ Digital computers operate only with binary numbers. Inside a digital calculator which is also a type of digital computer, when you enter $8+7=,$ you get the answer displayed as $15.$ But clearly, $8,7,$ as well as $15$ are not binary numbers rather they are decimal numbers. Even the operators $+,$ and $=$ are not the binary numbers. Have you ever thought about different steps taken by the calculator while adding two decimal numbers?

Suggest the basic schematic block diagram, to show the steps taken by the calculator after entering $8+7=,$ till getting the output as $15.(4$M$)($BL$-4)$