Consider a computer system that stores a floating-point numbers with 16-bit…
2007
Consider a computer system that stores a floating-point numbers with 16-bit mantissa and an 8-bit exponent, each in two’s complement. The smallest and largest positive values which can be stored are
- A.
1 × 10 -128and 215× 1015
- B.
1 × 10 -256and 215× 10255
- C.
1 × 10 -128and 215× 10127
- D.
1 × 10 -128and 215- 1 × 10127
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Correct answer: D
The 8-bit exponent in two's complement ranges from -128 to +127. The 16-bit mantissa in two's complement has a maximum positive value of 2^15 - 1. Therefore, the smallest positive value is 1 * 2^-128 and the largest positive value is (2^15 - 1) * 2^127.
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