Question

Perform the binary addition :

$(11001)_{2}+(10011)_{2}$

Answer 1

hi mate

here is your answer

Binary addition

1)Always keep in mind=

0+0 =0

1+0=1 or 0+1 = 1

1+1 = 10

Now

11001

(+)10011

--------------------

101100



so, 101100 is your answer.

hope it helps

BE BRAINLY///

Answer 2

$\underline{\underline{\Huge{\textbf{Concept Behind:}}}}$

$\maltese$ The order of adding bits is same as that of Decimal Addition i.e., The order will be from the $\textsf{Least Significant Bit (LSB)}$ to $\textsf{Most Significant Bit (MSB)}$

$\maltese$ The following table shows Sum and Carry bits that will be obtained on performing 2-bit Binary Addition for all possible cases is given below:

(Since there are $\textit{2- bits}$ and each bit can have $\textit{2 values}$ (either 0 or 1), total possible cases = $\textbf{ 2^2= 4 }$)

$\center\begin{array}{|c|c|c|c|}\cline{1-4}\sf Bit-1&\sf Bit-2&\bf Sum&\bf Carry\\\cline{1-4}0&0&0&0\\0&1&1&0\\1&0&1&0\\1&1&0&1\\\cline{1-4}\end{array}$

$\maltese$ A carry generated, $\textit{if any}$, is also to be added to the two bits (addend bits) and the sum is noted below the bit and the carry is to be forwarded to the side of more weighted bit.

$\maltese$ The Resultant Sum and Carry bits obtained on performing binary addition of 3-bits for all possible cases is given below:

(Since there are $\textit{3- bits}$ and each bit can have 2 values (either 0 or 1), total possible cases = $\textbf{ 2^3= 8 }$)

$\center\begin{array}{|c|c|c|c|c|}\cline{1-5}\sf Bit-1&\sf Bit-2&\sf Bit-3&\bf Sum&\bf Carry\\\cline{1-5}0&0&0&0&0\\0&0&1&1&0\\0&1&0&1&0\\0&1&1&0&1\\1&0&0&1&0\\1&0&1&0&1\\1&1&0&0&1\\1&1&1&1&1\\\cline{1-5}\end{array}$



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

$\begin{minipage}{7cm}\center \begin{array}{ccccccc}\textcircled1&&&\textcircled1&\textcircled1&\\&1&1&0&0&1\\+&1&0&0&1&1\end{array}\\\rule{4cm}{\fboxrule}\\\! \center \! \! \! \begin{array}{ccccccc}1&\; \, 0&\: 1\: &\: 1\; &0\; &\; 0\end{array}\end{minipage}$



$\underline{\LARGE{\textbf{Verification:}}}$

To verify the result,

$\blacktriangleright$ The given binary Numbers and the result of the binary addition are to be converted into decimal numbers.

$\blacktriangleright$ If the sum of the equivalent decimal numbers is equal to the decimal equivalent of the result of binary addition, then it is said that there is no error in the binary addition and the obtained result is the required Result.

$\bullet\\ \begin{aligned}\bf (11001)_{2}&=(1\times 2^4)+(1\times 2^3)+0+0+(1\times 2^0)\\&= 16+8+1\\&=25\end{aligned}$

$\bullet\\ \begin{aligned}\bf(10011)_{2}&= (1\times 2^4)+0+0+(1\times 2^1)+(1\times 2^0)\\&=16+2+1\\&=19\end{aligned}$

$\textsf{Adding these decimal equivalents,}\\\sf\textsf{25+19 = 44}$

$\bullet\\ \begin{aligned}\bf (101100)_{2}&=(1\times 2^5)+0+(1\times 2^3)+(1\times 2^2)+0+0\\&= 32+8+4\\&=44\end{aligned}$

$\textsf{Which is equal to the sum of Decimal}\\\textsf{Equivalents of the given binary Numbers.}$

$\underline{\textit{Hence Verified}}$




$\blacksquare \mathsf{(11001)_{2}+(10011)_{2}\: = \: }\LARGE{\underline{\Large{\mathbf{(101100)_{2}}}}}$