$2.$

$($a$)$ Construct a truth table for a half$-$adder, which adds two bits, A and

B together, to produce the sum bit $($S$)$ and the carry bit $($C$).$ Draw the

logic circuit diagram for the half$-$adder using only the basic logic

gates, i$.$e$.,$ AND gate, OR gate and NOT gate.

$($b$)$ Show diagrammatically how the concept of a half$-$adder can be

extended to realise a full$-$adder.

$($c$)$ State the purpose of a digital flip$-$flop and show, using the flip$-$flop$$s

circuit diagram, how this purpose is achieved.

$($d$)$ Explain what is meant by the term integrated circuit $($IC$)$ or a chip,

and describe the four classes of chips. Comment briefly on how the

chip technology contributed into the evolution of the digital

computers.

$($e$)$ Explain the implementation and performance differences between

static RAM $($SRAM$)$ and dynamic RAM $($DRAM$).$ State where each

type of memory is used in a computer as a result of their differences.