Question

Add the binary numbers. $$ 1101+101100+11011011 $$

   Add the binary numbers.
$$
1101+101100+11011011
$$

Discrete Mathematics

Discrete Mathematics

Richard Johnsonbaugh 8th Edition

Chapter 5, Problem 28

Instant Answer

Solved by Expert Ahmad Reda

01/27/2023

Step 1

We will align them vertically and add them bit by bit from right to left. \[ \begin{array}{c} \phantom{+}1101 \\ + \phantom{0}101100 \\ \hline \phantom{0}111001 \end{array} \] Show more…

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Add the binary numbers. $$ 1101+101100+11011011 $$

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Key Concepts

Binary Number System

This is a numeral system that uses only two symbols, 0 and 1, to represent any number. Each digit's value depends on its position, which corresponds to a power of 2. Understanding this system is crucial for performing and interpreting arithmetic operations in binary, particularly in computer science and digital electronics.

Binary Addition

This is the process of adding two or more binary numbers by following specific rules: 0+0=0, 0+1=1, and 1+1=10 (which means 0 with a carry of 1). It involves aligning the numbers by their least significant bits and adding digit by digit, managing any carry-overs that occur, similar to the addition process in the decimal system.

Positional Representation

This concept refers to the method of representing numbers where the position of each digit conveys its value multiplied by a power of the base (2 in the case of binary). It is fundamental to understanding how numbers are structured and manipulated in various numeral systems, including during addition.

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