Binary to Octal Conversion: Meaning, Differences, Solved Examples

Content Curator

Binary to Octal Conversion is the conversion of a number from base-8 to base-2 by using either direct or indirect methods. Each octal digit can convert into 3 digit binary representation. To change a binary number into an octal number, we first have to convert it into a decimal number or we can directly convert the binary number to an octal number.

Read Also: Natural Numbers

Table of Content

Binary Number System
Octal Number System
Difference between Binary, Octal, and Decimal Number System
Things to Remember
Sample Questions

Key Terms: Binary, Octal, Decimals, Number Systems, Hexadecimal, Decimal to Binary Converter

Binary Number System

[Click Here for Sample Questions]

The binary number is a computer language that is coded with 0&1 and its base is 2. The binary number system helps the students to understand the positional number system in which 2 is the base number and only 0 and 1 are the required numbers, instead of 10 numbers which are required in a decimal system. As it is a straightforward solution in the digital world, the binary number system is used in all modern technologies and computer-based devices.

Decimal

(84)₁₀ = 8x10¹ + 4x10⁰

=8x10 + 4x1

= 80+4

=84

Octal Number System

(124)₈

= 1x8² +2x8¹ + 4x8⁰

= 1x64 + 2x8 +4x1

= 64 + 16 + 4 = 84

Check Important Notes for Binary to Decimal Formula

Steps For Conversion Of Decimal To Binary

Binary to Decimal

Recognize the binary number
Convert binary to decimal and multiply every digit by 2n. n will be set at the right.
Answer will be the decimal number which is given by the binary number.

Decimal to Binary

it will be divided by 2
Reminder
Two steps has to be continued till the quotient is zero
Reminders should be written in reverse form.

After converting from binary to decimal, convert the equation from binary to decimal number.

Check Also: Types of Relations

Octal Number System

[Click Here for Sample Questions]

An octal number system is also a form of representing numbers. It is a coding number that requires 0 to 7, which we can also say as (10)octal. 8 and 9 are not a part of the octal number system. But it has the value power i.e. 8.

Decimal

In the decimal system each point is a part of 10.

(84)₁₀ = 8x10¹ + 4x10⁰

= 8x10 + 4x1

= 80+4

=84

Octal number system

(124)₈

= 1x8² +2x8¹ + 4x8⁰

= 1x64 + 2x8 +4x1

= 64 + 16 + 4 = 84

Conversion Of Decimal To Octal

As you will divide the number 84/8 it will give the reminder as 4 and quotient as 10.
10 will be divided by 8 it will give the reminder as 2 and quotient 1
Quotient 1 will be divided by 8 it will give the reminder 1 and quotient 0

Gather the remainder in the reciprocal form you will get 1,2,4.

From the above, it is learned that

Decimal (84)₁₀ = Octal (124)₈= Binary (I0I0I00)₂

Check More: Types of Functions

Steps For Conversion Of Binary To Octal

The following solution is the conversion of decimal numbers to octal numbers with the division of 8.

Decimal (93)₁₀

Then we have to follow the steps according to the question

As you will divide the number 93/8 it will give the reminder as 5 and quotient as 11.
5 will be divided it will give the reminder as 5 and 11 and quotient.
Quotient 11 will be divided by 8 it will give the reminder 3 and quotient 1
Quotient 1 will be divided by 8and it will give the reminder 1 and quotient 0

Gather the remainder in the reciprocal form you will get 1,3,5.

Decimal (93)₁₀=Octal (135)₈

And the last method would be

Converting a binary number to a decimal group

Recognize the binary no
All the 0 to 1, in sets of 3 are from the right side of the group
Add 0 to the left if it does not form a group of 3

Convert the binary number(I0III0I)2 to an octal number

(I0III0I)₂ = (1X2⁶)+ (0X2⁵) + (1X2⁴) + (1X2³) + (0X2¹) + (1X2⁰)

= 64+0+16+8+4+0+1

=93

= (I0III0I)² = (93)₁₀

Binary digit arrange as per following three-bit in a clubbed manner

= (001011101)₂ Binary

= ( 1 3 5 )₈ Octal

You can get the accurate number by tallying the binary to octal conversion by following this table:

OCTAL 0	BINARY 0
1	01
2	010
3	011
4	100
5	101
6	110
7	111

Read More: Binary Operations

Difference between Binary, Octal, And Decimal Number Systems

[Click Here for Sample Questions]

Key differences between binary, octal, and decimal number systems are:

DECIMAL	BINARY	OCTAL
It uses the digits like 0,1,2,3,4,5,6,7,8,9	It only uses two digits 0 and 1	It uses the eight digits 0,1,2,3,4,5,6,7
It is based on base 10 and it gives the power 10	It has only two values for 2 digits i.e. 0 and 1	It has values which the power of 8
Decimal has the base of power 210	Binary has a base of 21	Octal has the base of 8 or 23

Things to Remember

[Click Here for Sample Questions]

Convert the binary to octal
Solve the numerical with the following steps
Octal formula - 0,1,2,3,4,5,6,7
Binary formula - 000,001,010,011,100,101,110,111
Decimal formula - 0,1,2,3,4,5,6,7,8,9

Also Read: Complex numbers and Quadratic equations

Sample Questions

Ques. Convert binary number (001100101101110)2(001100101101110)2 to the octal number (5 Marks)

Ans. Write the 3-bit binary number which is mentioned in binary number according to the table i.e 1, 4, 5, 0, 5, 6

Therefore, (001100101101110)2(001100101101110)2 = (145056)8

Ques. Convert binary number 10010110 into octal number. (5 Marks)

Ans. First convert this into decimal number

= (10010110)₂

= 1x2⁷+0x2⁶+0x2⁵+1x2⁴+0x2³+1x2²+1x2¹+0x2⁰ = 128+0+0+16+0+4+2+0 = (150)₁₀

After that, convert it into octal number = (150)₁₀

= 2x8²+2x8¹+6x8⁰

= (226)₈ which is answer

Ques. Convert (0.675)10 to binary. (3 Marks)

Ans.

0.675 × 2 = 1.350	1
0.350 × 2 = 0.700	0
0.700 × 2 = 1.400	1
0.400 × 2 = 0.800	0
0.800 × 2 = 1.600	1
1 0.600 × 2 = 1.200	1
0.200 × 2 = 0.400	0

Ques. Convert (0.675)10 to octal. (3 Marks)

Ans.

0.675 × 8 = 5.400	5
0.400 × 8 = 3.200	3
0.200 × 8 = 1.600	1
0.600 × 8 = 4.800	4
0.800 × 8 = 6.400	6

Ques. Conversion of the binary number 1010101₂ to the octal number system. (5 Marks)

Ans. Use the method to convert the binary number into an octal number.

We will convert the given binary number to a decimal number.

= (1010101)₂

= (1 x 26⁶) + (0 x 25⁵ ) + (1 x 24⁴) + (0 x 23³) + (1 x 22²) + (0 x 21¹) + (1 x 20⁰)

= 64 + 0 + 16 + 0 + 4 + 0 + 1= 85(010101)₂

= 85₁₀

We will be dividing 85 by 8, we will get the remainder 5 and quotient 10.
Again we will divide 10 by 8, we will get remainder 2 and quotient 1.
Again we will divide 1 by 8, we will get remainder 1 and quotient 0.
Now collect the remainders in reverse order i.e. 1, 2, and 5.
Therefore, the octal number is 1258

Ques. Conversion of 13/10 to binary. (3 Marks)

Ans.

13/2 = 6 quotient and 1 remainder
6/2 = 3 quotient and 0 remainder
3/2 = 1 quotient and 1 remainder
1/2 = 0 quotient and 1 remainder

gather the remainder in order and we get the number I0II2

13₁₀ = I0II2

Ques. Conversion of binary number 10010110 into octal number. (5 Marks)

Ans. 13₁₀

= (10010110)₂

= 1x2⁷+0x2⁶+0x2⁵+1x2⁴+0x2³+1x2²+1x2¹+0x2⁰

= 128+0+0+16+0+4+2+0

= (150)₁₀

Then, we will convert it into an octal number

= (150)₁₀

= 2x8²+2x8¹+6x8⁰

= (226)₈ which is the correct answer

Ques. Conversion binary number 1010111100 into octal number. (5 Marks)

Ans. = (1010111100)₂

= (001 010 111 100)₂

= (1 2 7 4)₈

= (1274)₈

So, the correct answer is (1274)₈

Ques. Convert binary number 0110 011.1011 into octal number. (3 Marks)

Ans. = (0110 011.1011)₂

= (0 110 011 . 101 1)₂

= (110 011 . 101 100)₂

= (6 3 . 5 4)₈

= (63.54)₈

So, the correct answer is(63.54)₈

Ques. Conversion of octal number (121)₈ to decimal form. (3 Marks)

Ans. (121)₈ = 1 x 8² + 2 x 8¹ + 1 x 8⁰

(121)₈ = 1 x 64 + 2 x 8 + 1 x 1

(121)₈ = 64 + 16 + 1

Therefore the correct answer is (121)₈= (81)₁₀

Mathematics Related Links:
Perimeter of a Parallelogram	Angle Between Two Vectors	Polynomial Important Questions
Sin 180 Degrees	Area of Sector	Tan 0 Degrees
Quadrant	Polynomial Formula	Variance
Binary Subtraction Rules	Real-Valued Function	Relations and Functions

Binary to Octal Conversion: Meaning, Differences, Solved Examples

Binary Number System

Decimal

Octal Number System

Steps For Conversion Of Decimal To Binary

Octal Number System

Decimal

Octal number system

Conversion Of Decimal To Octal

Steps For Conversion Of Binary To Octal

Difference between Binary, Octal, And Decimal Number Systems

Things to Remember

Sample Questions

CBSE X Related Questions

1.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

4.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

5.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

6.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

Comments

SUBSCRIBE TO OUR NEWS LETTER

Binary to Octal Conversion: Meaning, Differences, Solved Examples

Binary Number System

Decimal

Octal Number System

Steps For Conversion Of Decimal To Binary

Octal Number System

Decimal

Octal number system

Conversion Of Decimal To Octal

Steps For Conversion Of Binary To Octal

Difference between Binary, Octal, And Decimal Number Systems

Things to Remember

Sample Questions

CBSE X Related Questions

1.Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

2.The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

4.Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent. Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

5.PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

6.Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
Prove that $14 - 2\sqrt{3}$ is an irrational number, given that $\sqrt{3}$ is irrational.

2.
The dimensions of a window are $156\text{ cm} \times 216\text{ cm}$. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.

3.
If the zeroes of a polynomial p(x) are $-3$ and 8, then p(x) equals

4.
Assertion (A) : The system of linear equations $3x - 5y + 7 = 0$ and $-6x + 10y + 14 = 0$ is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.

5.
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If OP = 13 cm, then find the length AB and PA.

6.
Two dice are rolled together. The probability of getting an outcome $(x, y)$ where $x \gt y$, is