Question

Sum of the binary number
(1101.101), and ( 111.011), is​

Answer 1

Given - Number for which sum has to be found -

(1101.101) and ( 111.011)

Find - Sum of given numbers

Solution - To find sum of binary numbers, several rules have to be followed. Rules are -

1. sum of zero and one is one
2. sum of zero and zero is zero
3. sum of one and one is ten
4. sum of three one's is eleven.

Adding the numbers -

1101.101

+ 111.011

10101.000

Hence, the sum of given binary numbers is - 10101.000.

Answer 2

$Sum \: of \: (1101.101_{2})\:and\: ( 111.011_{2})$

$= \Big(2^{3}+2^{2}+0\times 2^{1}+1\times 2^{0} +\frac{1}{2} + \frac{0}{2^{2}}+\frac{1}{2^{3}} \Big)+ \Big( 2^{2}+2^{1}+2^{0} + \frac{0}{2}+\frac{1}{2^{2}}+\frac{1}{2^{3}}\Big) \\=\Big(8+4+1+\frac{1}{2}+\frac{1}{8} \Big)+\Big( 4+2+1+\frac{1}{4}+\frac{1}{8}\Big)\\=( 8+4+0+1+0.5+0+0.125)+(4+2+1+0+0.25+0.125)\\= 13.625+7.375\\= 21_{10}$

$= 10101_{2}$

Therefore.,

$\red{ Sum \: of \: (1101.101_{2})\:and\: ( 111.011_{2})}$

$\green {= 10101_{2}}$

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