Question

what is result of following operation(4623.56)10+ (110011.11)2whare (110011.11(2 mean that 110011.11as a number express in base 2​

Answer 1

SOLUTION :

TO DETERMINE

The result of the operation

$\sf{}{(4623.56)}_{10} \: + \: {(110011.11)}_2$

PROCESS

STEP : 1

Write down the given two numbers

STEP : 2

Express them in same system ( Either in binary or in decimal system )

STEP : 3

Add the converted numbers

EVALUATION

Here the numbers

$\sf{}{(4623.56)}_{10} \: \: and \: \: {(110011.11)}_2$

are in decimal and binary system respectively

Now we express them in same system ( Here we choose Decimal system )

$\sf{} {(110011.11)}_2$

$= \sf{}{( {2}^{5} + {2}^{4 } + 0 +0 + {2}^{1} + {2}^{0} + {2}^{ - 1} + {2}^{ - 2} )}_{10}$

$= \sf{}{( {2}^{5} + {2}^{4 } + 0 \times {2}^{4} +0 \times {2}^{3} + {2}^{1} + {2}^{0} + {2}^{ - 1} + {2}^{ - 2} )}_{10} \:$

$= \sf{}{(32 + 16 + 2 + 1 + 0.5 + 0.25)}_{10}$

$= \sf{(51.75)_{10} }$

Now addition is done as below

$\sf{}4623.56 \: + \: 51.75 \: = \: 4675.31$

FINAL RESULT

$\sf{}{(4623.56)}_{10} + {(110011.11)}_2 = {(4675.31)}_{10}$

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