# 128 in Binary

In math, we follow a standard form to represent a number. We call it the number system.

We have different types of number systems in Math.

The binary number system is one of the most common systems to be used. This system uses only two digits $$0$$ and $$1$$

Thus, the numbers in this system have a base $$2$$

$$0$$ and $$1$$ are called bits.

In this mini lesson, we will explore the world of 128 in binary. We will walk through the answers to the questions like what is meant by converting 128 from decimal to binary, and how to convert 128 from decimal to binary number.

## What Is Meant By Converting 128 From Decimal to Binary?

$$128_{10}$$ is a decimal representation. Converting 128 from decimal to binary means to write or represent 128 using 2 bits only, which are 0 and 1

To convert $$128_{10}$$ in binary, we need to change the base from 10 to 2

$$128_{10}$$ in binary is $$10000000_{2}$$

## How to Convert 128 From Decimal to Binary Number?

Let us look at the steps showing the conversion of 128 from decimal to binary.

Step-1

Identify the base of the required number. In this case, the base of 128 is 10, i.e., $$128_{10}$$.

Step-2

Divide the given number 128 by the base of the required number, i.e. 2

Step-3

Note down the quotient and the remainder.

Step-4

Divide the number 128 until we get the quotient to be less than the base which is 2

Step-5

Read all the remainders including the last quotient from bottom to top.

(Note: digits marked in the green boxes represent the binary form of 128.)

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

$$128_{10}$$ in binary is $$10000000_{2}$$

Important Notes
• In the word binary, the meaning of the initials "Bi" is two. For example, a 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, $$128_{10}$$

## Solved Examples

Let us have a look at the solved examples on $$128_{10}$$ in binary, to understand the difference between decimal to binary and binary to decimal conversion without using a decimal to binary converter.

 Example 1

Jamie is trying her hands on number system conversion. She needs guidance in converting $$129_{10}$$ into the binary system. Help Jamie with the correct steps.

Solution

$$129_{10}$$ is in the decimal system.

Jamie needs to follow the following steps:

I) Identify the base of the required number, ie., 2

II) Divide the given number 129 by the base of the required number, i.e, $$129 \div 2$$

III) Note down the quotient and the remainder.

IV) Divide the number 129 until we get the quotient to be less than 2

V) Read all the remainders including the last quotient from bottom to top.

Repeat this process for every quotient until we get a quotient which is less than 2

 $$\therefore$$ $$129_{10}$$$$=$$ $$10000001_{2}$$
 Example 2

Hary is trying to convert $$120_{10}$$ into the binary system (base- $$2$$).What process should he use?

Solution

$$120_{10}$$ is in the decimal system.

Hary needs to follow the following steps:

I) Identify the base of the required number, ie., 2

II) Divide the given number 120 by the base of the required number, i.e, $$120 \div 2$$.

III) Note down the quotient and the remainder.

IV) Divide the number 120 until we get the quotient to be less than 2

V) Read all the remainders including the last quotient from bottom to top.

Repeat this process for every quotient until we get a quotient which is less than 2

 $$\therefore$$ $$120_{10}$$ $$=$$ $$1111000_2$$
 Example 3

Help Ron in converting the decimal number $$76_{10}$$ to a system with 1 and 0 bits.

Solution

$$76_{10}$$ is in the decimal system.

This needs to be converted to binary.

Ron needs to follow the following steps:

I) Identify the base of the required number, ie., 2

II) Divide the given number 76 by the base of the required number, i.e, $$76 \div 2$$

III) Note down the quotient and the remainder.

IV) Divide the number 76 until we get the quotient to be less than 2

V) Read all the remainders including the last quotient from bottom to top.

Repeat this process for every quotient until we get a quotient which is less than 2

 $$\therefore$$  $$76_{10}$$ $$=$$ $$1001100_2$$

## 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.

Challenging Question
We use 0-9 numbers for decimal and 0 & 1 bits for binary. Similarly, in the octal system, we use 0-7. Can you follow the same process and convert the following from decimal to octal?
a) $$130_{10}$$
b) $$102_{10}$$
c) $$111_{10}$$
d) $$1012_{10}$$

## Let's Summarize

The mini-lesson targeted the fascinating concept of 128 in binary. The math journey around 128 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.

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.

## 1. What is the binary number system based on?

The binary number system is based on the following essential key terms:

• The binary number system uses only two digits: $$0$$ and $$1$$
• The numbers in this system have a base $$2$$
• $$0$$ and $$1$$ are called bits.
• $$8$$ bits together make a byte.
• The data in computers is stored in terms of bits and bytes.

For example:

$$10001_2, 111101_2, 1010101_2$$ are some examples of numbers in the binary number system.

## 2. What is $$2^7$$ in binary?

Here $$2^7=128$$. The binary digit for $$128_{10}$$ is $$10000000_{2}$$

## 3. What does 10101 mean in decimal?

The meaning of $$10101_{2}$$ in decimal is $$21_{10}$$.

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