#Number System

Question

Assuming 6-bit 2's complement binary representation the largest number that can be subtracted from (-15) without causing overflow is?

Answer 1

Given that 6-bits and 2's complement form representation

therefore we can represent -32 to +31 decimal numbers, therefore beyond this range it cause overflow

Given that subtracting from -15 doesn't cause overflow

let x is your required number,

∴ -15-x can't cause overflow ===> -15-x ≥ -32 and  -15-x ≤ 31

 

1)  -15-x ≥ -32

-x ≥ -32+15 ===> -x ≥ -17 ====> x ≤ 17 ---------> For largest take 17

 

2) -15-x ≤ 31

-x ≤ 31+15 ===> -x ≤ 46 ===> x  ≥ -46 ----------> For lowest take -

But Note that -46 is can not represented with 6 bit in 2's complement number...

∴ up to -32 only we can represent ===> x  ≥ -32 ----------> For lowest take -32

Comments

Shaik Masthan  

For largest take 17 

= 17+ 15 = 32

but range is -32 to 31 right

therefore it should be 16 right ??

For lowest take  = -32

because Number less then -32 is not represented in 6 bit

??

 

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i updated the answer

@Magma

read the question and answer clearly, it is saying subtracted from -15.

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Shaik Masthan  yes you're right thanks :D