Octal Number System - Free MCQ Practice Test with solutions, GATE EE Digital

The given hexadecimal number is: 100

To convert the given Hexadecimal number, first, we need to convert it into binary and then into octal.
Hexadecimal to binary: 0001 0000 0000
Binary to octal: To convert a binary number into octal, we need to make a group of three digits from right to left before the decimal pointer and left to right after the decimal pointer.
= 000 100 000 000
= 0400 = 400

• Octal Number System: The octal number system has only eight (8) digits from 0 to 7. Every number (value) represents with 0,1,2,3,4,5,6 and 7 in this number system. The base or radix of the octal number system is 8 because it has only 8 digits.
• Binary Number System: A Binary number system has only two digits that are 0 and 1. Every number (value) represents 0 and 1 in this number system. The base or radix of the binary number system is 2 because it has only two digits.
• Decimal number system: The decimal number system has only ten (10) digits from 0 to 9. Every number (value) represents with 0,1,2,3,4,5,6, 7,8 and 9 in this number system. The base or radix of the decimal number system is 10 because it has only 10 digits.
• Hexadecimal number system: A Hexadecimal number system has sixteen (16) alphanumeric values from 0 to 9 and A to F. Every number (value) represents with 0,1,2,3,4,5,6, 7,8,9,A,B,C,D,E and F in this number system. The base or radix of the hexadecimal number system is 16 because it has 16 alphanumeric values. 

Concept:
Steps to convert decimal number to octal:
1) Write the given decimal number.
2) If the given decimal number is less than 8 the octal number is the same.
3) If the decimal number is greater than 7 then divide the number by 8.
4) Note the remainder, we get after division.
5) Repeat steps 3 and 4 with the quotient till it is less than 8.
6) Now, write the remainders in reverse order (bottom to top).
7) The resultant is the equivalent octal number to the given decimal number.

Calculation:
Given decimal number = 149
The long division method is as shown:

∴ The correct octal equivalent of 149 is 225

if the binary bits are less than three bits add 0 to the left hand side tp make a complete set

Octal to Binary Conversion:

• Every octal number is represented by a 3-bit binary equivalent.
• The table of binary representation for octal numbers (0 to 7) is given below:
  

Explanation:

• From the above table, the binary equivalent of 4 is 100.
• The binary equivalent of 7 is 111.
• The binary equivalent of 1 is 000

.
Hence, the binary equivalent of octal number 471 is (100111001)₂

Concept:

Following are the steps to convert decimal to octal:

• If the provided decimal number is less than the number 8 then the octal number is the same.
• If the provided decimal number is larger than 7 then divide it by number 8.
• take a note of the remainder, received after division
• Repeat step 2 and 3 with the quotient until it is less than 8
• Now, note the remainders in the reverse order (bottom to top)
• The resultant thus received is the equivalent octal number to the provided decimal number.

Explanation:

Hence, (432267)₁₀ = (1514213)₈

Octal Number: 

• The number to the Base 8 is called octal numbers.
• It uses the numbers from 0 to 7.
• The numbers 8 and 9 are not included in the octal number system.
• It is denoted by a8 where a is a number with digits 0 to 7.

Conversion from Binary to Octal:
An octal Equivalent of a binary number is obtained by grouping 3 bits from right to left.

So, Octal Equivalent: 321.

Binary to Octal code:

Concept:

There are only 8 digits (from 0 to 7) in the octal number system, so we can represent any digit of octal number system using only 3 bits as following below:

Follow below-mentioned steps to convert from Binary to Octal:
Step I: Select Binary Number.
Step II: Divide the binary digits into a group of three (starting from right) for the Integer part and start from left for the Fraction part.
Step III: Convert each group of three binary digits into an octal digit referring to the above table.

Calculation
Step I: Binary Number: 110101110
Step II: Divide the binary digits into the group of three (starting from the right) for the Integer part:
(010 101 110)
Step III: Convert each group of three binary digits into an octal digit referring to the above table:

(010 101 110)₂ = (256)₈

Decimal to Octal Conversion: If we want to change any octal number into decimal number we have to start multiplying the digits of the number from right hand side with increasing powers of 8 staring from 0 and finally summing up all the products.

• An octal number system has a base of 8.
• Digits from 0 to 7 are used to express an octal number.
• Each octal number converts to 3 binary digits.

This is explained in the following table: