Q $2($a$)$

$[6$ Marks$]$

$($i$)$ Study the three schematics in Figure $2$a$.$ Determine whether the resistor in each schematic is a properly placed pullup or pulldown resistor and indicate what the output to the Digital Circuit will be when the switch is open and closed in each case. $[4$ marks$]$

$($ii$)$ Also, why are resistors required when working with LEDs, and what exact function do they perform? $[2$ marks$]$

Q $2($b$)$

$[11$ Marks$]$

Please answer the following questions about the two's complement:

i$.$ Why is the two's complement still important to computers today?

ii$.$ Determine the decimal equivalent value of the two's complement binary number $\backslash (11110101\_\{2\}\backslash )$ on an $8-$bit digital computer.

iii. What is the two's complement of the decimal number $6$ in a digital system where all numbers are represented by four bits, and in a digital system where all numbers are represented by eight bits?

iv$.$ What are the largest most positive and the largest most negative numbers that can be represented on a $5-$bit and on a $16-$bit computer?

v$.$ Describe how overflow occurs in this context and how it can be detected.