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Convert the following unsigned decimal values to their equivalent 8-bit binary representation Show your work. а. b. 3 C. 7

Convert the following unsigned decimal values to their equivalent 8-bit binary representation Show your work. а. b. 3 C. 7

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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# Converting Unsigned Decimal Values to 8-bit Binary Representation In this exercise, we will convert several unsigned decimal values to their equivalent 8-bit binary representation. This process involves expressing each decimal number as a binary number using 8 digits, where each digit is a power of 2. Let's go through each of the given numbers: ### a. Decimal: 0 - **Binary:** 00000000 - **Explanation:** The decimal number 0 is represented in binary as all zeros. ### b. Decimal: 3 - **Binary:** 00000011 - **Explanation:** - \( 3 = 2^1 + 2^0 \) - Binary representation is 11, padded to 8-bits: 00000011. ### c. Decimal: 7 - **Binary:** 00000111 - **Explanation:** - \( 7 = 2^2 + 2^1 + 2^0 \) - Binary representation is 111, padded to 8-bits: 00000111. ### d. Decimal: 16 - **Binary:** 00010000 - **Explanation:** - \( 16 = 2^4 \) - The binary representation is 10000, padded to 8-bits: 00010000. ### e. Decimal: 127 - **Binary:** 01111111 - **Explanation:** - \( 127 = 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 \) - The binary representation is 1111111, padded to 8-bits: 01111111. ### f. Decimal: 255 - **Binary:** 11111111 - **Explanation:** - \( 255 = 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 \) - The binary representation is 11111111. By converting these numbers, you can see the systematic approach of binary representation where each position represents a power of 2, starting from \(2^0\) on the right. Each binary digit (bit) can either increase or not increase the total value
Transcribed Image Text:# Converting Unsigned Decimal Values to 8-bit Binary Representation In this exercise, we will convert several unsigned decimal values to their equivalent 8-bit binary representation. This process involves expressing each decimal number as a binary number using 8 digits, where each digit is a power of 2. Let's go through each of the given numbers: ### a. Decimal: 0 - **Binary:** 00000000 - **Explanation:** The decimal number 0 is represented in binary as all zeros. ### b. Decimal: 3 - **Binary:** 00000011 - **Explanation:** - \( 3 = 2^1 + 2^0 \) - Binary representation is 11, padded to 8-bits: 00000011. ### c. Decimal: 7 - **Binary:** 00000111 - **Explanation:** - \( 7 = 2^2 + 2^1 + 2^0 \) - Binary representation is 111, padded to 8-bits: 00000111. ### d. Decimal: 16 - **Binary:** 00010000 - **Explanation:** - \( 16 = 2^4 \) - The binary representation is 10000, padded to 8-bits: 00010000. ### e. Decimal: 127 - **Binary:** 01111111 - **Explanation:** - \( 127 = 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 \) - The binary representation is 1111111, padded to 8-bits: 01111111. ### f. Decimal: 255 - **Binary:** 11111111 - **Explanation:** - \( 255 = 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 \) - The binary representation is 11111111. By converting these numbers, you can see the systematic approach of binary representation where each position represents a power of 2, starting from \(2^0\) on the right. Each binary digit (bit) can either increase or not increase the total value
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