binary representation

Question

pls someone explain

How to left shift this number ?

1010110<<2

Answer 1: shifting to the left means adding extra 0's as rightmost bits so in this case it means 101011000 now digit will be 1011000 

but 1010110 represents 86 in decimal and left shift by 2 means multiply with 4 to the decimal number and now result 344 =101011000 now m confused ?

Comments

@joshi_nitish
 it means we have to ignore the  first two bits due to overflow condition ?And the method for shifting bits by multiplication /division by 2 is only suitable if no overflow condition holds ?
@Bikram Sir  @Debashish pls clear this

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see, 86=1010110, which require minimum of 7 bits, now if you perform any left shift, MSB bits will be lost..
but if you store 86 in 9 bits i.e 001010110, the bits will be not lost till <<2, similiarly if you store 86 in 10 bits i.e 0001010110, the bits will be not lost till <<3.....and so on.
got it???

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@ joshi_nitish

 86=1010110

if 1010110<<2 that means add 2 zeros at rightmost part 101011000 due to this MSB will lost by 2 bits , final value is=1011000=88

if I am applying multiplication method answer is different that is 344. (86*4)101011000 which is 9 bit (overflow)

m not getting these two different answers :(

Answer 1

Left shift means : The number to the left of the operator is shifted the number of places specified by the number to the right.

like 1010110<<2 

it would be after left shift 101011000

In general shifting N places left is the same as multiplying by 2 to the power N (written as 2^N)

A left shift 1 place is the same as multiplying by 2

A left shift 2 place is the same as multiplying by 4

see this example , number is 00100101

shift left 2 places

input	0	0	1	0	0	1	0	1
result	1	0	0	1	0	1	0	0

Comments

like same when shift left 3 places

for input      00100101 

it would be  00101000

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@Bikram Sir

like 1010110<<2   (1010110=86) if I am using multiplication method  then answer should be directly 86*4=344 and binary representation of this 101011000.(correct solution )

 if I want to represent this 1010110 number into 8 bit number (after left shift by 2),it means the MSB bits which is 10 (101011000) will be automatically removed ?

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if I want to represent this 1010110 number into 8 bit number (after left shift by 2),it means the MSB bits which is 10 (101011000) will be automatically removed ?

Yes left two bits are removed automatically .

Like that number is  0101 0110  ( 8 bit ) after left shift by 2 it will be 0101 1000  ( 8 bit) 

and MSB is a single bit like in 01011000 MSB is 0 

The MSB in an 8-bit binary number represents a value of 128 decimal. The LSB represents a value of 1.

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got it :)