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What is the range of decimal values of a 9 bit signed 2's complement number system?

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Final answer:

The range of decimal values for a 9-bit signed 2's complement number system is from -256 to 255, with the most significant bit indicating the sign.

Step-by-step explanation:

Range of Decimal Values in a 9-bit Signed 2's Complement

The range of decimal values for a 9-bit signed 2's complement number system can be determined by considering how signed numbers are represented in the 2's complement system. In such a system, the most significant bit (MSB) represents the sign of the number, where '0' stands for positive and '1' for negative. For a 9-bit number, there are 8 bits remaining to represent the magnitude of the number.

The largest positive number is when the MSB is '0' and all other bits are '1', which is 2^8 - 1 or 255. The largest negative number is when all bits are '1', which in 2's complement represents -1. However, the smallest negative number occurs when the MSB is '1' and all other bits are '0', which is -2^8 or -256. Therefore, the range is from -256 to 255, inclusive.

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