# How many 1's are there in the binary form of 8*1024 + 3*64 + 3

4

#### srinivas

• Jan 1st, 2006

how should we get 4

#### anubhav

• Aug 2nd, 2006

Actually we first have to multiply then we willl get the ans as 8387 but this ans is in decimal now we willl convert it into binary form. we will get 000011000011 i hope all of you know how to convert decimal to binary so finally ans is 4

#### priyanka

• Nov 14th, 2006

i dont see how answer is 4

it should be 8...using the double-dabble simple method of converting decimal to binary by repetedly dividing by 2, we get 1 as remainder 8 times. becoz the result is 8387 in decimal

and 10110011101001 in binary

#### Manish

• Jun 24th, 2007

3*64=11*1000000 Answer will contain 2 one's
3=11

Hence total 5 one's and not 4.

#### ganita Profile Answers by ganita

• Feb 7th, 2011

Consider the binary representations of all three terms:

(1) 8*1024 = 2^3*2^10 = 2^13 which is 1 followed by 13 zeroes.

(2) 3*64 = 2*64 + 1*64 = 2^7 + 2^6 which is 1 followed by 7 zeros added to 1 followed by six zeroes.

(3) 3 = 2^1 + 2^0 and equals 1 followed by 1 zero added to 1 followed by no zeroes.

Since all the ones have different place values, and none overlap, we do not have any 'carrys', and there is a total of FIVE ONES in the binary representation.

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