$($a$)$ In order to understand digital system, one must know basic binary arithmetic

since it is essential in all digital computers and in many other types of digital

systems. Such arithmetic is addition, subtraction, multiplication and division.

Convert the numbers into binary and solve the arithmetic $($show complete

steps$).$

i$.,7_{10}+{45}_{10}$

$(3$ marks$)$

ii$.,{43}_{16}+4E_{16}$

$(3$ marks$)$

iii. $,{20}_{16}+C{D}_{16}$

$(3$ marks$)$

$($b$)$ The NAND gate is significant because any Boolean function can be

implemented by using a combination of NAND gates. The NAND technology

has been employed in various kind of product, including solid$-$state drive.

i$.$ Using AND, NOT and OR gate, sketch the logic circuit for the function

$F=B.C\frac{+}{b}ar(B)\frac{+}{b}ar(C),$ where $F$ is an output while $B$ and $C$ are inputs.

$(6$ marks$)$

ii$.$ Represent the function in $($i$)$ using NAND gates.In order to understand digital system, one must know basic binary arithmetic

since it is essential in all digital computers and in many other types of digital

systems. Such arithmetic is addition, subtraction, multiplication and division.

Convert the numbers into binary and solve the arithmetic $($show complete

steps$).$

i$.,7_{10}+{45}_{10}$

$(3$ marks$)$

ii$.,{43}_{16}+4E_{16}$

$(3$ marks$)$

iii. $,{20}_{16}+C{D}_{16}$

$(3$ marks$)$