1. What are the 16-bit 1's and 2's complements of the following binary numbers? a. 10000 b. 100111100001001
1. What are the 16-bit 1's and 2's complements of the following binary numbers? a. 10000 b. 100111100001001
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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**Exercise: Computing 1's and 2's Complements**
**Objective:** Learn how to calculate 16-bit 1's and 2's complements of binary numbers.
**Problem Statement:**
Determine the 16-bit 1’s and 2’s complements for the following binary numbers:
a. 10000
b. 100111100001001
c. 0100111000100100
**Instructions:**
1. **1's Complement:** Flip each bit of the binary number, changing all 0s to 1s, and all 1s to 0s.
2. **2's Complement:** Take the 1's complement of the binary number, then add 1 to the least significant bit (rightmost bit).
**Example Calculation:**
Let's calculate the 1's and 2's complement for option (a):
- **Original Binary Number:** 0000 0000 0001 0000 (padded with leading zeros for 16 bits)
- **1's Complement:** 1111 1111 1110 1111
- **2's Complement:** 1111 1111 1111 0000 (Add 1 to the 1's complement)
Now, apply these steps to the other options and check your results.
---
This instructional text guides students through understanding and solving the problem."
Transcribed Image Text:Sure, here is the transcription formatted for an educational setting:
---
**Exercise: Computing 1's and 2's Complements**
**Objective:** Learn how to calculate 16-bit 1's and 2's complements of binary numbers.
**Problem Statement:**
Determine the 16-bit 1’s and 2’s complements for the following binary numbers:
a. 10000
b. 100111100001001
c. 0100111000100100
**Instructions:**
1. **1's Complement:** Flip each bit of the binary number, changing all 0s to 1s, and all 1s to 0s.
2. **2's Complement:** Take the 1's complement of the binary number, then add 1 to the least significant bit (rightmost bit).
**Example Calculation:**
Let's calculate the 1's and 2's complement for option (a):
- **Original Binary Number:** 0000 0000 0001 0000 (padded with leading zeros for 16 bits)
- **1's Complement:** 1111 1111 1110 1111
- **2's Complement:** 1111 1111 1111 0000 (Add 1 to the 1's complement)
Now, apply these steps to the other options and check your results.
---
This instructional text guides students through understanding and solving the problem.
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