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Question 4 What is the decimal value for a signed hexadecimal A1E? The answer should be scale to a WORD size storage location. O 2590 O 30 O-2590 O-2589 < Previous lys

Question 4 What is the decimal value for a signed hexadecimal A1E? The answer should be scale to a WORD size storage location. O 2590 O 30 O-2590 O-2589 < Previous lys

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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### Question 4 **What is the decimal value for a signed hexadecimal A1E? The answer should be scaled to a WORD size storage location.** - [ ] 2590 - [ ] 30 - [ ] -2590 - [ ] -2589 **Explanation:** In a computer's memory, data can be signed or unsigned depending on how the bits are interpreted. "WORD size storage location" typically refers to 16 bits, or 2 bytes, of data. When dealing with signed hexadecimal numbers, the most significant bit (MSB) is used to determine the sign of the number—0 for positive and 1 for negative. Hexadecimal `A1E` can be broken down as follows: - `A` represents `1010` in binary - `1` represents `0001` in binary - `E` represents `1110` in binary When put together: `A1E` = `1010 0001 1110` If `A1E` is interpreted as a 16-bit signed integer, the MSB is `1`, indicating it is a negative number. To find the decimal value, you can convert the hexadecimal to binary and then use two's complement to get the signed value. Here is a step-by-step process: 1. **Convert Hexadecimal to Binary:** A = 1010 \ 1 = 0001 \ E = 1110 \ Together: `A1E` = `1010 0001 1110` 2. **Determine if the Value is Negative:** Since the MSB is `1`, the number is negative. 3. **Find the Two's Complement:** - Invert the bits: `0101 1110 0001` - Add `1` to the least significant bit (LSB): `0101 1110 0001 + 1` = `0101 1110 0010` 4. **Convert Binary to Decimal:** `0101 1110 0010` in binary is `2586` in decimal. Therefore, the negative value is `-2586`. **Answer Selection:** - The appropriate answer is not listed correctly. - In such cases, students may want to double-check or possibly report the question if there's an error in the provided options. The closest mistaken value can
Transcribed Image Text:### Question 4 **What is the decimal value for a signed hexadecimal A1E? The answer should be scaled to a WORD size storage location.** - [ ] 2590 - [ ] 30 - [ ] -2590 - [ ] -2589 **Explanation:** In a computer's memory, data can be signed or unsigned depending on how the bits are interpreted. "WORD size storage location" typically refers to 16 bits, or 2 bytes, of data. When dealing with signed hexadecimal numbers, the most significant bit (MSB) is used to determine the sign of the number—0 for positive and 1 for negative. Hexadecimal `A1E` can be broken down as follows: - `A` represents `1010` in binary - `1` represents `0001` in binary - `E` represents `1110` in binary When put together: `A1E` = `1010 0001 1110` If `A1E` is interpreted as a 16-bit signed integer, the MSB is `1`, indicating it is a negative number. To find the decimal value, you can convert the hexadecimal to binary and then use two's complement to get the signed value. Here is a step-by-step process: 1. **Convert Hexadecimal to Binary:** A = 1010 \ 1 = 0001 \ E = 1110 \ Together: `A1E` = `1010 0001 1110` 2. **Determine if the Value is Negative:** Since the MSB is `1`, the number is negative. 3. **Find the Two's Complement:** - Invert the bits: `0101 1110 0001` - Add `1` to the least significant bit (LSB): `0101 1110 0001 + 1` = `0101 1110 0010` 4. **Convert Binary to Decimal:** `0101 1110 0010` in binary is `2586` in decimal. Therefore, the negative value is `-2586`. **Answer Selection:** - The appropriate answer is not listed correctly. - In such cases, students may want to double-check or possibly report the question if there's an error in the provided options. The closest mistaken value can
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