In decimal system there are 10 digits 0, 1, 2, 3, . . . till 9. Similarly, there is a system which has only 3 digits 0, 1 and 2. Numbers represented in such systems are called base 3 or trinary numbers. A = 389 + 1 is a number in the decimal system. B is the trinaryequivalent of this number. How many zeros are there in B ?
Question
In decimal system there are 10 digits 0, 1, 2, 3, . . . till 9. Similarly, there is a system which has only 3 digits 0, 1 and 2. Numbers represented in such systems are called base 3 or trinary numbers. A = 389 + 1 is a number in the decimal system. B is the trinaryequivalent of this number. How many zeros are there in B ?
Solution
To find the trinary equivalent of the decimal number A = 389 + 1, we need to convert it into base 3.
First, let's convert A into base 3.
To do this, we divide A by 3 and keep track of the remainders.
389 divided by 3 is 129 with a remainder of 2.
129 divided by 3 is 43 with a remainder of 0.
43 divided by 3 is 14 with a remainder of 1.
14 divided by 3 is 4 with a remainder of 2.
4 divided by 3 is 1 with a remainder of 1.
1 divided by 3 is 0 with a remainder of 1.
Now, let's write the remainders in reverse order.
The trinary equivalent of A = 389 + 1 is 111202.
To find the number of zeros in B, we need to count the number of zeros in the trinary number 111202.
In this case, there are 2 zeros in B.
Similar Questions
The number of 3-digit numbers in all in the base-10 system is
The number system having just these two digits – 0 and 1 – is called?A) Decimal Number SystemB) Binary Number SystemC) Octal Number SystemD) Hexadecimal Number System
The difference of the number of 4 digit numbers and the number of 3 digit numbers in base 10 system is
How many three-digit numbers in base 10 are three-digit numbers in base 8 but not in base 7?
A number in a base is said to be a special number if it is equal to the sum of its own digits each raised to the power of the number of digits. A number in base ‘b’ can have digits from 0 to b-1. By default the numbers used by humans is to base 10 and called as decimal number system. A number ‘n’ from decimal number system can be converted to any base ‘b’ by repeated division of ‘n’ by ‘b’ and writing reminder of each division in reverse order. For example, number 24 is converted to base 3 as shown below:
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.