Question

Computer Science Question !!!

Convert
$2ab_{16}$
to it's decimal equivalent.

Please answer it!

Answer 1

$\underline{\underline{\Huge{\textbf{Question:}}}}$

$\sf\textsf{Convert 2ab_{16} to it's decimal equivalent.}$



$\underline{\underline{\Huge{\textbf{Solution:}}}}$

$\underline{\Large{\textbf{Hexadecimal\: Number\: System}}}$

$\sf\textsf{Hexadecimal Number system is a Base-16 Positional Numeral sytem}$

$\sf\textsf{It consists of 16 distinct symbols:}$
$\sf\textsf{which are 0 - 9 (and are same as in decimal Number system)}$
$\sf\textsf{and A - F (or a - f) (which represents 10 - 15 in the decimal Number system)}$

$\textit{The following table shows the same:}$

$\begin{tabular}{|c|c|}\cline{1-2}\bf Decimal & \bf Hexadecimal\\ \bf Number System & \bf Number System\\\cline{1-2}0&0\\1&1\\2&2\\3&3\\4&4\\5&5\\6&6\\7&7\\8&8\\9&9\\&\\A&10\\B&11\\C&12\\D&13\\E&14\\F&15\\\cline{1-2}\end{tabular}$



It overcomes the problem of $\sf\textsf{errors in reading or writing the long bit binary numbers}$
such as 16 or 32-bit as it treats 4-bits or a single nibble and considers it's equivalent Hexadecimal Number.

$\sf\textit{This also makes conversion between binary}\\\sf\textit{and Hexadecimal Number system simpler.}$

Due to this, Most of the today's digital systems or computers use the Hexadecimal Number system.



$\underline{\Large{\textbf{steps \: for \: hexdecimal \: to \: decimal \: conversion}}}$

$\large{\mathbf{1:}} \\ \: \sf\textsf{Each digit of the Hexadecimal Number}\\\sf\textsf{is multiplied with the positional weight of the digit.}$

$\large{\mathbf{2:}} \\ \sf \textsf{Adding each of these multiplied values} \\ \sf \textsf{gives decimal equivalent of the given Hexadecimal Number.}$



Given,

$2ab_{16}$ 

$\begin{tabular}{|c|c|c|c||}\cline{1-4} \bf Hexadecimal Number & 2 & A & B\\\cline{1-4}\bf Bit Position (n) &2&1&0\\\cline{1-4}\bf Weight Factor ( 16^{n} )& 16^{2} & 16^{1} & 16^{0} \\\cline{1-4}\bf Bit \times 16^{n} &2 \times16^{2} &10 \times16^{1} &11 \times16^{0} \\\cline{1-4}\bf Decimal Value&512&160&11\\\cline{1-4}\end{tabular}\begin{tabular}{|c|}\cline{1-2}\bf Decimal number\cline{1-2}\\512+160+11\\=683\\\\\cline{1-2}\end{tabular}$

$\implies (2ab)_{16}= (683)_{10}$



$\therefore$

$\blacksquare \: \: \textsf{Decimal Equivalent of (2ab)_{16} = \underline{\Large{\textbf{683}}}}$

Answer 2

ANSWER:-------

 16 distinct symbls: which are 0 - 9 (and are same as in decimal Number system)\sf\textsf{which are 0 - 9 (and are same as in decimal Number system)}which are 0 - 9 (and are same as in decimal Number system)and A - F (or a - f) (which represents 10 - 15 in the decimal Number system)\sf\textsf{and A - F (or a - f) (which represents 10 - 15 in the decimal Number system)}and A - F (or a - f) (which represents 10 - 15 in the decimal Number system)The following table shows the same:\textit{The following table shows the same:}The following table shows the same:

hope it helps:---T!—!ANKS!!!