64 in Binary

In this mini-lesson, we will learn how to convert 64 to binary by understanding the rules for converting numbers from decimals to binary and how to apply them while solving problems. We will also discover interesting facts around them.

Humans can communicate with each other by means of languages.

Americans communicate with each other in English, French people talk in French, while Indians have their conversations in Hindi or English.

But have you ever thought of how two machines talk to each other?

Or how humans communicate with machines?

Humans communicate with machines

Machines can only understand one language, i.e., binary language.

Machines convert every form of inputs from the user to binary language and then perform the required task.

For example, if you write "Hello World" on your keyboard, your computer first converts this into a binary language and then displays your text on the screen.

Hello world on a computer screen

The binary language contains only two numbers, 0 and 1

These numbers 0 and 1 are called bits.

Let us find an answer to the question "what is 64 in binary" on this page.

Lesson Plan 

What Is Meant by 64 In Binary?

If someone asks you to write the number 64, you simply write it like this – 64

But what if you are asked to write 64 in decimal form?

\(64_{10}\) is the decimal representation of 64, where 10 is referred to as the base of the number.

64 in decimal

Converting 64 from decimal to binary means to write or represent \(64\) using \(2\) bits only, i.e., \(0\) and \(1\)

For converting 64 from decimal to binary, we need to change the base from \(10\) to \(2\)

decimal number system has a base 10 and uses 0-9

Binary number system has a base 2 and uses only 0 and 1

\(64_{10} \text{ in binary is } 1000000_{2}\)

How to Convert 64 From Decimal to Binary?

Let us look at the steps showing the conversion of 64 from decimal to binary.

Step 1:- Identify the base of the required number. In this case, the base of \(64\) is \(10\), i.e., \(64_{10}\)

Step 2:- Divide the given number 64 by the base (2) and note down the quotient and the remainder in the “quotient-remainder” form.

Repeat this process (dividing the quotient again by the base) until we get the quotient to be less than 2

decimal to binary method

Therefore  \(64_10 = 1000000_2 \)

Convert 64 from Binary to Decimal

Converting \(1000000_2\) to decimal

Step 1: Identify the base of the given number.

Here, the base of \(1000000_2\) is 2

Step 2: Multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.

The exponents should start with \(0\) and increase by \(1\) every time we move from right to left.

Since the base here is \(2\), we multiply the digits of the given number by \(2^0, 2^1, 2^2,...\) from right to left. 

binary to decimal

Step 3: We just simplify each of the above products and add them. 

converting 64 to decimal from binary

Here, the sum is the equivalent number in the decimal number system of the given number.

\(\therefore 1000000_2 = 64_{10}\)
important notes to remember
Important Notes
  • In the word binary, the meaning of the initials "Bi" is two. For example, bike (\(2\) wheels).
  • The binary system is represented by base \(2\). For example, \(1101000_2\)
  • The decimal system is represented by base \(10\). For example, \(300_{10}\)
  • To convert a number from decimal system to a binary system:
    Divide the given number by the base of the required number and note down the quotient and the remainder in the “quotient-remainder” form repetitively until we get the quotient to be less than the base. The given number in the decimal number system is obtained just by reading all the remainders and the last quotient from bottom to top.

Solved Examples 

Example 1

 

 

Mathew is trying to convert twice the number 64 from decimal to binary. What process should he use?

Solution

Twice of 64 is \(64 \times 2 = 128\)

\(128_{10}\) is in the decimal system.

Mathew needs to divide \(128\) by \(2\) and note down the quotient and the remainder.

He should repeat this process for every quotient until he gets a quotient that is less than \(2\)

converting 128 from decimal to binary

\(\therefore\) \(128_{10}\) \(=\) \(10000000_2\)
Example 2

 

 

Help Ron in converting the binary number \(100000_{2}\) to a decimal number.

Solution

\(100000_{2}\) is in the binary system.

Ron needs to multiply each digit of the given number, starting from the rightmost digit, with the exponents of the base.

The exponents should start with \(0\) and increase by \(1\) every time as we move from right to left.

Since the base here is \(2\), Ron multiplies the digits of the given number by \(2^0, 2^1, 2^2,...\) from right to left.

converting binary to decimal

\(\therefore\)  \(100000_{2}\) \(=\) \(32_{10}\)
 
Challenge your math skills
Challenging Question
Just like we use digits from 0-9 for decimal and 0 & 1 bits for binary, in the octal system, we use 0-7. Can you follow the same process and see if you can convert the numbers below from binary to octal.
a) \(1000_{2}\)
b) \(10_{2}\)
c) \(1100_{2}\)
d) \(1001_{2}\)

Interactive Questions 

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

 
 
 
 

Let's Summarize

The mini-lesson targeted the fascinating concept of 64 in binary. The math journey around 64 in binary starts with what a student already knows, and goes on to creatively crafting a fresh concept in the young minds. Done in a way that is not only relatable and easy to grasp but will also stay with them forever. Here lies the magic with Cuemath.

About Cuemath

At Cuemath, our team of math experts is dedicated to making learning fun for our favorite readers, the students!
Through an interactive and engaging learning-teaching-learning approach, the teachers explore all angles of a topic.
Be it worksheets, online classes, doubt sessions, or any other form of relation, it’s the logical thinking and smart learning approach that we, at Cuemath, believe in.


Frequently Asked Questions(FAQ's)

1. What is the binary number of 64? 

Binary number of 64 is \(\text{1000000}\)

2. What does 10101 mean in decimal? 

\(10101_2\) means \(21_{10}\) in decimal.

3. How do you write 63 in binary?

Binary number of 63 is \(\text{111111}\)

4. What is the binary of 37?

\(37_{10}\) can be written as \(100101_{2}\) in binar
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