/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 12 Convert \((1100001100011)_{2}\) ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 4: Problem 12

Convert \((1100001100011)_{2}\) from its binary expansion to its hexadecimal expansion.

Short Answer

Expert verified
1863

Step by step solution

01

- Group the Binary Digits

Begin by grouping the binary digits into sets of four, starting from the right: (1, 1000, 0110, 0011).
02

- Add Leading Zeros

If a group has fewer than four digits, add leading zeros to make it a complete group of four digits: (0001, 1000, 0110, 0011).
03

- Convert Each Group to Hexadecimal

Next, convert each 4-bit binary group to its hexadecimal equivalent: 0001 鈫� 1 1000 鈫� 8 0110 鈫� 6 0011 鈫� 3.
04

- Combine the Results

Combine all the hexadecimal digits obtained in the previous step to get the final answer: (1, 8, 6, 3), which can be written as 1863.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

binary number
A binary number is a number expressed in the base-2 numeral system. The system uses only two digits, 0 and 1. Each binary digit is known as a bit.
Computers use binary numbers because they can easily represent the two states of a switch (on and off) with 0s and 1s.
Understanding binary numbers is fundamental in fields like computer science and electrical engineering.
The binary numeral system works similarly to the decimal (base-10) system, but with only two digits. Each bit in a binary number represents an increasing power of 2, starting from the rightmost bit, which represents 2^0.
hexadecimal number
A hexadecimal number is a number expressed in the base-16 numeral system. This system uses sixteen distinct symbols: 0-9 to represent values zero to nine, and A-F to represent values ten to fifteen.
Hexadecimal numbering is often used in computing as a more human-friendly representation of binary-coded values. It's easier to read and write large binary numbers when they are expressed in hexadecimal.
For example, the binary number 11111111 can be expressed more conveniently as FF in hexadecimal.
The hexadecimal system works similarly to the decimal and binary systems, but it uses base-16. Each digit represents an increasing power of 16, starting from the rightmost digit: \((16^0, 16^1, 16^2, ...)\).
number system conversion
Number system conversion involves changing a number from one base to another. In particular, converting between binary and hexadecimal is common in computing.
To convert a binary number to hexadecimal:
  • Group the binary digits into sets of four, starting from the right.
  • Add leading zeros if the leftmost group has fewer than four digits.
  • Convert each group to its hexadecimal equivalent.

For example, to convert the binary number 1100001100011 to hexadecimal:
  • Group the digits: (1, 1000, 0110, 0011).
  • Add leading zeros: (0001, 1000, 0110, 0011).
  • Convert each group: 0001 鈫� 1, 1000 鈫� 8, 0110 鈫� 6, 0011 鈫� 3.
  • Combine the results: 1863.
Number system conversions are crucial for understanding different data representations and their uses in technology and mathematics.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Describe the extended Euclidean algorithm using pseudocode.

Show that the integer \(m\) with two's complement representation \(\left(a_{n-1} a_{n-2} \ldots a_{1} a_{0}\right)\) can be found using the equation \(m=-a_{n-1} \cdot 2^{n-1}+a_{n-2} 2^{n-2}+\cdots+a_{1} \cdot 2+a_{0}\).

Prove Euler's criterion, which states that if \(p\) is an odd prime and \(a\) is a positive integer not divisible by \(p\) , then $$ \left(\frac{a}{p}\right) \equiv a^{(p-1) / 2}(\bmod p) $$

Prove that the product of any three consecutive integers is divisible by \(6 .\)

To break a Vigen猫re cipher by recovering a plaintext message from the ciphertext message without having the key, the first step is to figure out the length of the key string. The second step is to figure out each character of the key string by deter- mining the corresponding shift. Exercises 21 and 22 deal with these two aspects. Once the length of the key string of a Vig猫nere cipher is known, explain how to determine each of its characters. Assume that the plaintext is long enough so that the frequency of its letters is reasonably close to the frequency of letters in typical English text.
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.