Database System Concepts
Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Question
**Task: Converting Decimal Numbers to 8-Bit Signed Binary Using 2's Complement** **Objective:** Convert the following decimal numbers into 8-bit signed binary numbers using the 2’s complement form. **Given Numbers:** - -127 - 127 **Explanation:** *2’s Complement Method:* 1. Identify the magnitude of the number in binary. 2. For negative numbers, invert the digits (0->1 and 1->0) to get the 1’s complement. 3. Add 1 to the resulting binary number to get the 2’s complement. 4. Ensure the result fits within 8 bits, including the sign bit. **Process:** 1. **-127 in 2’s Complement:** - Positive 127 in binary: `01111111` - Invert all bits: `10000000` - Add 1 to the inverted number: `10000000 + 1 = 10000001` - Thus, -127 in 8-bit 2’s complement form is: `10000001` 2. **127 in Binary:** - Positive 127 in binary is already `01111111` (the most significant bit is 0, indicating a positive number). By using the above method, we accurately convert these decimal values to binary form suitable for use in digital systems utilizing 2's complement notation.
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Transcribed Image Text:**Task: Converting Decimal Numbers to 8-Bit Signed Binary Using 2's Complement** **Objective:** Convert the following decimal numbers into 8-bit signed binary numbers using the 2’s complement form. **Given Numbers:** - -127 - 127 **Explanation:** *2’s Complement Method:* 1. Identify the magnitude of the number in binary. 2. For negative numbers, invert the digits (0->1 and 1->0) to get the 1’s complement. 3. Add 1 to the resulting binary number to get the 2’s complement. 4. Ensure the result fits within 8 bits, including the sign bit. **Process:** 1. **-127 in 2’s Complement:** - Positive 127 in binary: `01111111` - Invert all bits: `10000000` - Add 1 to the inverted number: `10000000 + 1 = 10000001` - Thus, -127 in 8-bit 2’s complement form is: `10000001` 2. **127 in Binary:** - Positive 127 in binary is already `01111111` (the most significant bit is 0, indicating a positive number). By using the above method, we accurately convert these decimal values to binary form suitable for use in digital systems utilizing 2's complement notation.
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