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Every integer has an equivalent representation in decimal and binary. Except for 0 and 1, the binary representation of an integer has more digits than its decimal counterpart. To find the number of binary digits bits corresponding to any given decimal integer, you could convert the decimal number to binary and count the bits.

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For example, the two-digit decimal integer 29 converts to the five-digit binary integer Sometimes you want to know, not how many bits are required for a specific integer, but how many are required for a d -digit integer — a range of integers. A range of integers has a range of bit counts. For example, four-digit decimal integers require between 10 and 14 bits. For any d -digit range, you might want to know its minimum, maximum, or average number of bits.

Those values can be computed directly as well. In this article, I will show you those calculations. All of the discussion assumes positive integers, although it applies to negative integers if you temporarily ignore their minus signs. An integer is an integer, independent of its base. For example:. For larger numbers, you could consult a table of powers of two to find the consecutive powers that contain your number.

To see why this works, think of the binary representations of the integers 2 4 through 2 5 — 1, for example. They are throughall possible 5-bit values. The above method can be stated another way: the number of bits is the exponent of the smallest power of two greater than your number.

You can state that mathematically as:. How many bits do numbers in this range require? It varies. For example, consider four-digit decimal integers. The number of bits varies between those extremes. For example, requires 11 bits, requires 12 bits, and requires 13 bits. Why does this occur? Because that single power of ten range spans all or part of five consecutive power-of-two ranges.

The minimum number of bits required for a d -digit integer is computed simply by using the specific number formula on the minimum d -digit value:. The maximum number of bits required for a d -digit integer is computed simply by using the specific number formula on the maximum d -digit value:. This allows us to use this more computationally efficient formula to the same effect:. The average number of bits required for a d -digit integer is the total number of bits required to represent all d -digit integers divided by the number of d -digit integers.By using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service.

Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up. Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How many bits needed to store a number Ask Question. Asked 7 years, 10 months ago.

Active 9 months ago. Viewed 19k times. Tanner Also you need a ceiling function in the end. For example IEEE floats are very well suited to store numbers that are powers of two, or relatively small numbers times a power of two. Active Oldest Votes. Brian M. Scott Brian M. Scott k 43 43 gold badges silver badges bronze badges. Sign up or log in Sign up using Google.

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how many bits to represent a number

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Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. How many bits needed to store a number Ask Question. Asked 7 years, 9 months ago. Active 9 months ago. Viewed 19k times. Tanner Also you need a ceiling function in the end.

For example IEEE floats are very well suited to store numbers that are powers of two, or relatively small numbers times a power of two.

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Representing Numbers with Bits

Wiki User That depends on the type and coding of the variable containing the number. Integer numbers are typically represented using Binary coding with 8, 16, 32, 64, or bits on most modern computers although occasionally more bits are used for special applications. Real numbers are typically represented using Floating Point coding with 32, 64, 80, or bits on most modern computers although graphics processors often use 16 bits and special applications sometimes use bits.

Complex numbers, being made of two Real numbers use twice as many bits as whatever type of Real number uses. Some numbers are represented in a coded Decimal format instead of Binary. Computers in the s through s have used as few as 6 bits to as many as 72 bits for numbers. It can be almost anything, I once wrote a special program that used more than 60, bits for a few numbers that required very high precision to get the correct answer.

That computer had variable wordlength hardware that supported such very wide words directly, but on modern computers which all have fixed wordlength hardware the same sized numbers can be handled using software arithmetic libraries. Related Questions Asked in Numbers How many bits are needed to represent decimal ? Asked in College Applications and Entrance Requirements Four bytes can represtent a decimal number between 0 and?

Four bytes represent 32 bits. Asked in Math and Arithmetic, Mathematical Finance, C Programming How many binary bits are required to represent the decimal number ? Asked in Math and Arithmetic, Calendar How many bits represent the days of the week?

In theory, 3 bits are enough to represent up to 8 23 combinations. Asked in Engineering, Computer Memory, Numbers What is the minimum number of bits required to represent the following decimal number ? Asked in Definitions What is a compression? Compression is a reduction in the number of bits needed to represent data. Asked in Math and Arithmetic What is the largest positive signed decimal number that can be represented by 8-bits? This is to Asked in Computer Networking How many address bits are required to represent a 32K memory?

how many bits to represent a number

Using 8 bits per pixel, how can representor 28 shades. Asked in Digital Cameras, Colors How many bits are needed to represent each color? Most modern digital cameras use 24 bits 8 bits per primary to represent a color. But more or less can be used, depending on the quality desired. Many early computer graphics cards used only 4 bits to represent a color.

Asked in Computer Terminology How many bits are used to represent a letter? Asked in Computer Terminology, Windows Vista 8 bits can represent how many different characters? There are possible values or characters in 8 bits. Asked in Math and Arithmetic How many binary bits are necessary to represent different numbers? Binary bits are necessary to represent different numbers in the sense that binary bits are represented in digital wave form.Challenge Level: Ready to expand.

Write a program that asks the user to enter a number of dots i.

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For example, the number 15 can be represented in 4 bits, but 16 requires 5 bits. You can work this out by starting with the number 1, and doubling it until it gives you a value more than the number you need to represent, so this program can be based on the earlier challenge to work out the number of dots on each card.

View full screen. Use block to repeat these steps until condition is true. Test your program with some values on the boundaries for example number 31 would need 5 bits and 32 needs 6 bits. Show solution. Display the value of bits as the output. Topics Printables About. Home Topics Binary numbers Display the number of bits needed to represent a number Display the number of bits needed to represent a number Challenge Level: Ready to expand.

This programming challenge is linked to the following lessons: Challenge 6. Students will be able to: Describe how variables store values and how they are used in your program.

Computer Science: Programming Explain what you need to consider if you are asking for an input from the end user. Computer Science: Programming Identify how and when to use a loop to repeat a set of instructions. Computer Science: Programming. Make variables called: "total number of dots" and set its value to the number entered by the end user. What it should look like For the input 19 the code will output: Please enter the number of dots: You will need 5 bits to store number This definition is not available in English, sorry!The log2 n logarithm in base 2 of n, which is the exponent to which 2 is raised to get n only integer and we add 1 find total bit in a number in log n time.

how many bits to represent a number

This article is contributed by Gyayak Jain. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

How To Convert Decimal to Binary

Writing code in comment? Please use ide. Count total bits in a number Find XOR of all elements in an Array Count maximum occurrence of subsequence in string such that indices in subsequence is in A. Given a positive number n, count total bit in it. Python3 program to find. This code is contributed by mits. Log number2.

WriteLine countBits num. Function to get no of bits. Write countBits i. Recommended Posts: Write an Efficient Method to Check if a Number is Multiple of 3 Find the Number Occurring Odd Number of Times Write an Efficient C Program to Reverse Bits of a Number Count set bits in an integer Count number of bits to be flipped to convert A to B Rotate bits of a number Compute modulus division by a power-ofnumber Find whether a given number is a power of 4 or not Add 1 to a given number Next higher number with same number of set bits Program to count number of set bits in an big array Count total set bits in all numbers from 1 to n Swap bits in a given number Binary representation of a given number Swap all odd and even bits.

Load Comments.The log2 n logarithm in base 2 of n, which is the exponent to which 2 is raised to get n only integer and we add 1 find total bit in a number in log n time. This article is contributed by Gyayak Jain.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute. See your article appearing on the GeeksforGeeks main page and help other Geeks. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Writing code in comment? Please use ide. Count total bits in a number Maximize the Expression Bit Manipulation Queries to find the count of integers in a range that contain the given pattern Count of N-bit binary numbers without leading zeros Maximum distance between two 1's in Binary representation of N.

Given a positive number n, count total bit in it. Python3 program to find. This code is contributed by mits. Log number2.

WriteLine countBits num. Function to get no of bits. Write countBits i. Recommended Posts: Write an Efficient Method to Check if a Number is Multiple of 3 Find the Number Occurring Odd Number of Times Write an Efficient C Program to Reverse Bits of a Number Count set bits in an integer Count number of bits to be flipped to convert A to B Rotate bits of a number Compute modulus division by a power-ofnumber Find whether a given number is a power of 4 or not Add 1 to a given number Next higher number with same number of set bits Program to count number of set bits in an big array Count total set bits in all numbers from 1 to n Swap bits in a given number Binary representation of a given number Swap all odd and even bits.

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