Write the following decimal numbers as 8-bit signed binary numbers, using 2's complement form -127 127
Write the following decimal numbers as 8-bit signed binary numbers, using 2's complement form -127 127
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
Problem 1PE
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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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