Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1 1 1 1 0 1 1 0 X 1 1

1 1 1 1 0 1 1 0 X 1 1

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.5: Determinants
Problem 89E
See similar textbooks
icon
Related questions
Question

Binary multiplication:

 

I need to double check my answer

### Binary Multiplication Example Let's consider an example of binary multiplication. Below, we have two binary numbers which are going to be multiplied: \[ \begin{array}{cccccc} & 1 & 1 & 1 & 0 & 1 \\ \times & 1 & 1 & 0 & 1 \\ \end{array} \] ### Explanation: We will be multiplying the binary number \(11101_2\) by the binary number \(1101_2\). 1. Arrange the two binary numbers, one below the other, ensuring they are aligned to the right. 2. Start from the least significant bit (rightmost bit) of the bottom number and, for each bit, multiply it by the entire top number. 3. If the multiplier's bit is 1, write down the top number shifted to the left by the bit's position (starting from 0). If the bit is 0, write down 0s (of the same length as the top number shifted by the bit's position). Here is a step-by-step breakdown of the multiplication: 1. **(Least Significant Bit on bottom number is 1):** - Write down the top number shifted by 0 positions: \(11101_2\). 2. **(Next Bit 0):** - Write down all 0's shifted by 1 position: \(00000_2\). 3. **(Next Bit 1):** - Write down the top number shifted by 2 positions: \(1110100_2\). 4. **(Next Bit 1):** - Write down the top number shifted by 3 positions: \(11101000_2\). Now, add up the results obtained from the multiplications: \[ \begin{array}{cccccccc} & & & & 1 & 1 & 1 & 0 & 1 \\ + & & & & 0 & 0 & 0 & 0 & 0 & 0 \\ + & & & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ + & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ &=&=&=&=&=&=&=&=&\\ & & 1 & 1 & 1 & 0 &
Transcribed Image Text:### Binary Multiplication Example Let's consider an example of binary multiplication. Below, we have two binary numbers which are going to be multiplied: \[ \begin{array}{cccccc} & 1 & 1 & 1 & 0 & 1 \\ \times & 1 & 1 & 0 & 1 \\ \end{array} \] ### Explanation: We will be multiplying the binary number \(11101_2\) by the binary number \(1101_2\). 1. Arrange the two binary numbers, one below the other, ensuring they are aligned to the right. 2. Start from the least significant bit (rightmost bit) of the bottom number and, for each bit, multiply it by the entire top number. 3. If the multiplier's bit is 1, write down the top number shifted to the left by the bit's position (starting from 0). If the bit is 0, write down 0s (of the same length as the top number shifted by the bit's position). Here is a step-by-step breakdown of the multiplication: 1. **(Least Significant Bit on bottom number is 1):** - Write down the top number shifted by 0 positions: \(11101_2\). 2. **(Next Bit 0):** - Write down all 0's shifted by 1 position: \(00000_2\). 3. **(Next Bit 1):** - Write down the top number shifted by 2 positions: \(1110100_2\). 4. **(Next Bit 1):** - Write down the top number shifted by 3 positions: \(11101000_2\). Now, add up the results obtained from the multiplications: \[ \begin{array}{cccccccc} & & & & 1 & 1 & 1 & 0 & 1 \\ + & & & & 0 & 0 & 0 & 0 & 0 & 0 \\ + & & & 1 & 1 & 1 & 0 & 1 & 0 & 0 \\ + & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \\ &=&=&=&=&=&=&=&=&\\ & & 1 & 1 & 1 & 0 &
Expert Solution
steps

Step by step

Solved in 2 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Integers
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
SEE MORE TEXTBOOKS