https://file.aiquickdraw.com/mathbot/file/1726693190312h6x80o91.jpg

The problem asks to convert the decimal number 77 (written as \(77_{10}\)) into its binary (base 2) equivalent.

To convert from decimal to binary, we can divide the number by 2 repeatedly and keep track of the remainders:

1. \( 77 \div 2 = 38 \) with remainder \(1\)
2. \( 38 \div 2 = 19 \) with remainder \(0\)
3. \( 19 \div 2 = 9 \) with remainder \(1\)
4. \( 9 \div 2 = 4 \) with remainder \(1\)
5. \( 4 \div 2 = 2 \) with remainder \(0\)
6. \( 2 \div 2 = 1 \) with remainder \(0\)
7. \( 1 \div 2 = 0 \) with remainder \(1\)

Now, writing the remainders from bottom to top gives the binary number: \(1001101_2\).

Thus, \(77_{10} = 1001101_2\).

Would you like further details or have any questions?

Here are 5 related questions for practice:
1. Convert \(45_{10}\) to binary.
2. What is \(1001011_2\) in decimal?
3. Convert \(100011_2\) to decimal.
4. What is the binary representation of \(128_{10}\)?
5. How do you convert a binary fraction like \(1101.01_2\) to decimal?

**Tip**: When converting from decimal to binary, always divide by 2 and track remainders from last to first!

Learn how to convert the decimal number 77 to its binary equivalent using division by 2. This guide provides a clear explanation of the process with step-by-step instructions, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation