0
bbb
In numbering systems greater than decimal (base 10), we use the lowercase letters of the alphabet, in order, to delineate values greater than 9 in a single place. Thus an "a" means that there are 10 of that place value, a "b" means 11, etc.
This is the equivalent of 11 * (12^2) + 11 * (12^1) + 11 * (12^0)
= (11)(144) + (11)(12) + (11) (1)
= 1584 + 132 + 11
= 1727 (base 10)
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What is the largest three-digit number base four?
The greatest value a digit can have in base for is 3. Thus the largest three-digit number in base for would be 333. In base 10, this number is 3x16 + 3x4 + 3 = 63 Therefore 63 is the largest digit that would be three digits in base 4.
How many 4 digit numbers are there?
In base ten, there are 9000 four digit number, the numbers are from 1000 to 9999. If you allow leading zeros, then there are 10000 numbers. [0000 - 9999]
What is the highest digit that can be used in each place value?
In the decimal number system, the highest valued digit is 9. The highest digit that ever appears in any one 'place' of a number is one less than the 'base' of the number. The numbers that everyone is most familiar with ... the numbers you see around you every day ... are numbers written in the 'decimal' system, using the 'base' of 10. So the highest digit in any one place is 9. 'Binary' numbers ... the form most used to represent numbers inside digital circuits and computers ... are constructed in base 2. So the highest digit in any one place is 1, and each of these numbers is just a string of 1's and zeros. Digits can be even higher than 9 in number systems that use other bases. For example, the hexadecimal system (often used in computer science to represent binary numbers) is base 16, so in that case the highest valued digit is "F" which has a value equivalent to 15 in a decimal representation. As an example, the number "FA" hexadecimal, has decimal value 15*16 + 10 = 250.
How many three-digit numbers are there in base 4?
If you allow leading zeros, then 4*4*4 = 64 If you don't allow leading zeros, then 3*4*4 = 48 (the numbers from decimal 16 to 63)
How many different telephone numbers of 7 digits can be formed if the first cannot be zero?
There are a number of issues with this question. Phone numbers are limited to more than just the first number not being 0. What about 9-1-1? What about 4-1-1, or 5-1-1, or 3-1-1? What about 1-Area-Number? What about 1-0-Carrier-country-1-city-number? What about the fact that some exchanges do not permit a 0 or a 1 as the second digit of the number? What about the fact that the sum of the first and third digits are constrained to not be certain sums? (The last two rules are to prevent older rule-base auto-long-distance dialing detection logic from misdetecting an area code.) What about constraints on the last four digits.With that said, and with only the constraints imposed by the question, i.e. ignoring these other known constraints, there are 9,000,000 different phone numbers in one exchange.
