For example, the decimal number 12 ( = $1 \times 10^1 + 2 \times 10^0$ ) is expressed as 14( = $1 \times 8^1 + 4 \times 8^0$) in the octal number system.
The decimal number 108 in the octal number system is
Decimal to Octal Conversion Explained
The question asks to convert the decimal number 108 (base-10) into its octal equivalent (base-8). The octal system uses digits 0 through 7.
Conversion Method: Division by Base
To convert a decimal number to octal, we repeatedly divide the decimal number by the target base (which is 8 for octal) and keep track of the remainders. The octal number is formed by the remainders read in reverse order (from bottom to top).
Step-by-Step Conversion of 108
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Divide the decimal number 108 by 8:
$108 \div 8 = 13 \text{ remainder } 4$
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Divide the quotient (13) by 8:
$13 \div 8 = 1 \text{ remainder } 5$
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Divide the quotient (1) by 8:
$1 \div 8 = 0 \text{ remainder } 1$
Final Octal Representation
Reading the remainders from bottom to top (1, 5, 4), we get the octal representation of the decimal number 108.
Therefore, decimal 108 is equivalent to octal 154.
Check: $154_8 = (1 \times 8^2) + (5 \times 8^1) + (4 \times 8^0) = (1 \times 64) + (5 \times 8) + (4 \times 1) = 64 + 40 + 4 = 108_{10}$.
Important Questions from Number System and Binary Codes
The binary equivalent of the decimal number 10 is __________.
The decimal number 76 in hexadecimal and BCD number system is respectively;
The binary equivalent of the decimal number 10 is __________.
The steps for subtracting two positive numbers (M−N) using (r−1)'s complement are:
(A) Add the minuend M to the (r−1)'s complement of the substrahend N.
(B) If an end carry occurs, add 1 to the least significant bit.
(C) If end carry does not occur, take the (r−1)'s complement of the number obtained in step A and place negative sign in front
(D) Take (r−1)'s complement of the number obtained in step B on step C.
Choose the correct answer from the options given below:
A number may be represented in various number systems. Arrange the following number systems in ascending order based on the number of bits needed to represent the same number.
A. Binary
B. Decimal
C. Hexadecimal
D. Octal
Choose the correct answer from the options given below
