2. the range of 8 - bit 2\'s complement numbers is 00000000 to 01111111 for post

Question

2. the range of 8 - bit 2's complement numbers is 00000000 to 01111111 for postive values and 10000000 to 11111111 for negative values.

These 8 bit binary words can be converted into two - digit hexadecimal expressions. in this case, what range of hexadecimal expressions represents positive numbers? what range represents negative numbers?

3.give an algebraic expression for the range of n bit 2's complement numbers

4. without converting a 2's complement arithmetic problem into decimal, how can validity be checked

Explanation / Answer

t's not. An unsigned byte (assuming 8-bit) is from 0 to 255.

The range of a signed byte using 2's complement is from -128 to 127, directly from the definition of 2's complement:

so is representation of -128 10000000 or 110000000 ?

In 8-bit, it's 10000000, in a hypothetical 9-bit representation it's 110000000.

Why not simply make the lower range -127 for 8 bits?

Artificially restricting the range to -127 wouldn't achieve very much; you'd be disallowing a perfectly valid value, and generally making code more complex (what else would you do with the bit pattern 10000000?).

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.