Question

What is the common property of DECIMAL, OCTAL, BINARY and HEXADECIMAL number systems???



C++ Computer science​

Answer 1

hi dude

The common property of the decimal, octal, binary and hexadecimal number system is that all of these can be converted to binary numbers.

All these numbers(hexadecimal, octal) are composed of numbers of binaries too.

Thus, they can be easily represented by a binary number system. Octals are base 8 numbers.

to be honest this ans is not mine one of the brinly users!!

hope it helps!!!

Answer 2

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

$\blacktriangleright$ The common Property of Binary, Octal, Decimal and Hexadecimal No. sytem is that all are $\textsf{Positional Numeral System}$ with Base-2, Base-8, Base-10 and Base-16 Respectively.

$\blacktriangleright$The $\textsf{allowed bits}$ for any position in the Number for a number system is equal to $\textbf{base}$ of that Number system.




$\maltese\; \textbf{Consider Binary number system}$

$\textsf{It is \textbf{Base-2} Positional Numeral System.}$

$\textsf{Here, the allowed bits are :}\\\textit{0 and 1}$

$\mathbf{Say (101)_{2}}$

$\begin{tabular}{|c|c|c|c||}\cline{1-4} \bf Binary Number & 1 & 0 & 1\\\cline{1-4}\bf Bit Position (n) &2&1&0\\\cline{1-4}\bf Weight Factor ( 2^{n} )& 2^{2} & 2^{1} & 2^{0} \\\cline{1-4}\bf Bit \times 2^{n} &1 \times2^{2} &0 \times2^{1} &1 \times2^{0} \\\cline{1-4}\bf Decimal Value&4&0&1\\\cline{1-4}\end{tabular}\begin{tabular}{|c|}\cline{1-1}\bf Decimal Number\\\cline{1-1}\\4+0+1\\=\bf 5&&\cline{1-2}\end{tabular}$




$\maltese\; \textbf{Consider Octal Number System}$

$\textsf{It is \textbf{Base-8} Positional Numeral System.}$

$\textsf{Here, the allowed bits are :}\\\textit{0 through 7}$

$\mathsf{Say (144)_{8}}$

$\begin{tabular}{|c|c|c|c||}\cline{1-4} \bf Octal Number & 1 & 4 & 4\\\cline{1-4}\bf Bit Position (n) &2&1&0\\\cline{1-4}\bf Weight Factor ( 8^{n} )& 8^{2} & 8^{1} & 8^{0} \\\cline{1-4}\bf Bit \times 8^{n} &1 \times8^{2} &4 \times8^{1} &4 \times8^{0} \\\cline{1-4}\bf Decimal Value&64&32&4\\\cline{1-4}\end{tabular}\begin{tabular}{|c|}\cline{1-1}\bf Decimal Number\\\cline{1-1}\\64+32+4\\=\bf 100&&\cline{1-2}\end{tabular}$




$\maltese\textbf{Consider Decimal Number System}$

$\textsf{It is \textbf{Base-10} Positional Numeral System.}$

$\textsf{Here, the allowed bits are :}\\\textit{0 through 9}$

$\mathsf{Say (765)_{10}}$

$\begin{tabular}{|c|c|c|c||}\cline{1-4} \bf Octal Number & 7 & 6 & 5\\\cline{1-4}\bf Bit Position (n) &2&1&0\\\cline{1-4}\bf Weight Factor ( 10^{n} )& 10^{2} & 10^{1} & 10^{0} \\\cline{1-4}\bf Bit \times 10^{n} &7 \times1/^{2} &6 \times10^{1} &5 \times10^{0} \\\cline{1-4}\bf Decimal Value&700&60&5\\\cline{1-4}\end{tabular}\begin{tabular}{|c|}\cline{1-1}\bf Decimal Number\\\cline{1-1}\\700+60+5\\=\bf 765&&\cline{1-2}\end{tabular}$




$\maltese\; \textbf{Consider hexadecimal Number System}$

$\textsf{It is \textbf{Base-16} Positional Numeral System.}$

$\textsf{Here, the allowed bits are :}\\\textit{0 through 9 and }\\\textit{A through F (or a through f)}$

$\mathsf{Say (1F4)_{16}}$

$\begin{tabular}{|c|c|c|c||}\cline{1-4} \bf Hexadecimal Number & 1 & F & 4\\\cline{1-4}\bf Bit Position (n) &2&1&0\\\cline{1-4}\bf Weight Factor ( 16^{n} )& 16^{2} & 16^{1} & 16^{0} \\\cline{1-4}\bf Bit \times 16^{n} &1 \times16^{2} &0 \times16^{1} &1 \times16^{0} \\\cline{1-4}\bf Decimal Value&256&240&4\\\cline{1-4}\end{tabular}\begin{tabular}{|c|}\cline{1-1}\bf Decimal Number\\\cline{1-1}\\256+240+4\\=\bf 500&&\cline{1-2}\end{tabular}$




$\blacksquare$Clearly, it is observed that each bit in the number is multiplied by the corresponding bit factor. The Sum of these values is equal to the $\textsf{Decimal Equivalent}$ of the considered No. of any Number system.