42 in Binary

Humans communicate with each other through various languages.

people talking

But have you ever wondered how two machines talk to each other, or how humans communicate with machines?

humans communicate with machines

Machines can only understand one language which is the binary language.

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

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

Hello world written 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 42 in binary' in this session.

In this mini-lesson, we will learn how to convert 42 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 some interesting facts around them.

100 in binary is cartoon image

Lesson Plan

What Is Meant By 42 In Binary?

If someone asks you to write the number 42, you simply write it as 42.

But what if you are asked to write 42 in the decimal form?

\(42_{10}\) is a decimal representation of 42, where 10 is referred to as the base of the number.

42 in decimal

Converting 42 from decimal to binary means to write or represent \(42\) using \(2\) bits, i.e., \(0\) and \(1\).

For converting 42 from decimal to binary, we need to change the base from \(10\) to \(2\).  

decimal number system has a base 2 and uses 0-9

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

\[42_{10} \text{ in binary is } 101010_{2}\]

43 in Binary

43 in binary is \(101011\).

13 in Binary

13 in binary is \(1101\).

47 in Binary

47 in binary is \(101111\).


How to Convert 42 From Decimal to Binary?

Let us observe the following steps which show the conversion of 42 from decimal to binary.

Step 1:- Identify the base of the required number. In this case, the base of \(42\) is \(10\), i.e., \(42_{10}\).

Step 2:- Divide the given number 42 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  \({42}_{10} = {101010}_{2}\)

Convert 101010 From Binary to Decimal

What does 101010 mean?

The answer to the question can be found by converting \(101010_2\) to decimal. So let's find out.

Step 1: Identify the base of the given number.

Here, the base of \(101010_2\) 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 always start with \(0\) and increase by \(1\) each time as we move from right to left.

Since the base here is \(2\), we need to 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 42 to decimal from binary

This sum (39) is the decimal form of the number given in binary.

\(\therefore 101010_2 = 42_{10}\)

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 the base \(2\). For example, \(1101000_2\).
  • The decimal system is represented by the base \(10\). For example, \(300_{10}\).

Solved Examples 

Example 1

 

 

Mathew wants to convert the double of 42 from decimal to binary. Can you help him?

Solution

The double of 42 is \(42 \times 2 = 84\).

\(84_{10}\) is in the decimal system.

Divide \(84\) by \(2\) and note down the quotient and the remainder.

Repeat this process for every quotient until we get a quotient which is less than \(2\).

converting 84 from decimal to binary

\(\therefore\) \(84_{10}\) \(=\) \(1010100_2\)
Example 2

 

 

Help Ron in converting the binary number \(10101_{2}\) to a decimal number.

Solution

\(10101_{2}\) is a binary number.

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

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

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

converting binary to decimal

\(\therefore\)  \(10101_{2}\) \(=\) \(21_{10}\)
 
Challenge your math skills
Challenging Question
Just like we use 0-9 numbers 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 following 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 42 in binary. The math journey around 42 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 not only it is relatable and easy to grasp, but also will 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(FAQs)

1. What is the binary number of 42?

The binary number of 42 is \(\text{101010}\).

2. What is 42 in binary 8 bit?

42 in binary 8 bit is \(\text{00101010}\).

Two zeros have been placed in the beginning to make a total of 8-bits (8 digits). 

3. What does 11111111 mean in decimal?

\(11111111_2\) means \(255_{10}\) in decimal.

4. How do you write 23 in binary?

\(23_{10}\) can be written as \(10111_{2}\) in binary.

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