Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form?

My attempt:

32 = 0100000 ( 1st zero - sign bit as positive)

So to represent +32 we need 7 bits

-32 = 1100000 (1st bit 1 - sign bit as negative)

So to represent -32 we need 7 bits

But answer is given as 6 bits to store -32 and 7 bits to store +32(positve case i understood, negative in my opinion it should be 7 bits). His reason - one 1 bit enough to represent negative number. I am confused. Please clarify here

Also i have following Questions:-

Can we say number of bits required to represent a negative number is strictly less than( or less than equal to) number of bits required to represent that corresponding positive number?

 

how can we generalise minimum number of bits required to represent a given positive and negative number say +N and -N in signed magnitude representation, signed 1's complement notation and signed two's compliment notation.

Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form?

My attempt:

32 = 0100000 ( 1st zero - sign bit as positive)

So to represent +32 we need 7 bits

-32 = 1100000 (1st bit 1 - sign bit as negative)

So to represent -32 we need 7 bits

But answer is given as 6 bits to store -32 and 7 bits to store +32(positve case i understood, negative in my opinion it should be 7 bits). His reason - one 1 bit enough to represent negative number. I am confused. Please clarify here

Also i have following Questions:-

Can we say number of bits required to represent a negative number is strictly less than( or less than equal to) number of bits required to represent that corresponding positive number?

how can we generalise minimum number of bits required to represent a given positive and negative number say +N and -N in signed magnitude representation, signed 1's complement notation and signed two's compliment notation.

Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form?

My attempt:

32 = 0100000 ( 1st zero - sign bit as positive)

So to represent +32 we need 7 bits

-32 = 1100000 (1st bit 1 - sign bit as negative)

So to represent -32 we need 7 bits

But answer is given as 6 bits. His reason - one 1 bit enough to represent negative number. I am confused. Please clarigy here

Also i have following Questions:-

Can we say number of bits required to represent a negative number is strictly less than( or less than equal to) number of bits required to represent that corresponding positive number?

how can we generalise minimum number of bits required to represent a given positive and negative number in signed magnitude representation, signed 1's complement notation and signed two's compliment notation.

I know that minimum number bits will be of order of logn to base 2. But exactly how much i am not able to think.

I know range of numbers in signed magnitude and signed one's complement is $-(2^{n-1} - 1) $ to $+(2^{n-1} - 1) $ while range of numbers in signed two complement representation is $-(2^{n-1}) $ to $+(2^{n-1} - 1) $

Minimum number of bits required to represent $(+32)_{base10}$ and $(-32)_{base10}$ in signed two's compliment form?

My attempt:

32 = 0100000 ( 1st zero - sign bit as positive)

So to represent +32 we need 7 bits

-32 = 1100000 (1st bit 1 - sign bit as negative)

So to represent -32 we need 7 bits

But answer is given as 6 bits to store -32 and 7 bits to store +32(positve case i understood, negative in my opinion it should be 7 bits). His reason - one 1 bit enough to represent negative number. I am confused. Please clarify here

Also i have following Questions:-

Can we say number of bits required to represent a negative number is strictly less than( or less than equal to) number of bits required to represent that corresponding positive number?

how can we generalise minimum number of bits required to represent a given positive and negative number say +N and -N in signed magnitude representation, signed 1's complement notation and signed two's compliment notation.