Understanding 2's Complement w/ 4 Bits

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In 2's complement representation with 4 bits, the range of numbers is from -8 to +7, rather than 0 to 15, because the system allocates half of the values for negative numbers. With 4 bits, a total of 16 different values can be represented, but 2's complement uses the highest bit as a sign bit, limiting the positive range. This means that while unsigned representation can show values from 0 to 15, 2's complement focuses on balancing positive and negative values. The confusion arises from misunderstanding the difference between unsigned magnitude and signed representation. Understanding this distinction clarifies why the range is limited in 2's complement.
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Why in 2's complement the range of numbers that can be represented with 4 bits are from -8 to +7? Wouldn't the numbers with 4 bits be till 15? I am confused.Please help me out.

-Thankyou
 
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With four bits, you can store 16 different values. You make them represent 0 through 15, which is called unsigned magnitude, or you can make them represent -8 through +7, which is called 2's complement. You cannot represent all the numbers from, say, -8 to +15, because you do not have enough bits.

- Warren
 

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