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How many bits needed to store a number $55^{2002}$ ?
My answer is $2002\;\log_2(55)$; is it correct?
J. W. Tanner
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asked Jun 19, 2012 at 11:55
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5
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The number of bits required to represent an integer $n$ is $\lfloor\log_2 n\rfloor+1$, so $55^{2002}$ will require $\lfloor 2002\; \log_2 55\rfloor+1$ bits, which is $11,575$ bits.
Added: For example, the $4$-bit integers are $8$ through $15$, whose logs base $2$ are all in the interval $[3,4)$. We have $\lfloor\log_2 n\rfloor=k$ if and only if $k\le\log_2 n<k+1$ if and only if $2^k\le n<2^{k+1}$, and that’s exactly the range of integers requiring $k+1$ bits.
answered Jun 19, 2012 at 12:01
Brian M. ScottBrian M. Scott
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5 in binary is 101. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits). We have used 3 bits to represent 5 in binary. In this article, let us learn how to convert the decimal number 5 to binary.
How to Convert 5 in Binary?
Step 1: Divide 5 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0.
5/2 = 2 | 1 |
2/2 = 1 | 0 |
1/2 = 0 | 1 |
Step 2: Write the remainder from bottom to top i.e. in the reverse chronological order. This will give the binary equivalent of 5.
Therefore, the binary equivalent of decimal number 5 is 101.
☛ Decimal to Binary Calculator
Let us have a look at the value of the decimal number 5 in the different number systems.
- 5 in Binary: 5₁₀ = 101₂
- 5 in Octal: 5₁₀ = 5₈
- 5 in Hexadecimal: 5₁₀ = 5₁₆
- 101₂ in Decimal: 5₁₀
Problem Statements:
What is 5 in Binary? - (Base 2) | (101)₂ |
What is 5 in Hexadecimal? - (Base 16) | (5)₁₆ |
What is 5 in Octal? - (Base 8) | (5)₈ |
Is 5 a Perfect Cube? | No |
Cube Root of 5 | 1.709976 |
Is 5 a Prime Number? | Yes |
Square Root of 5 | 2.236068 |
Is 5 a Composite Number? | No |
Is 5 a Perfect Square? | No |
FAQs on 5 in Binary
What is 5 in Binary?
5 in binary is 101. To find decimal to binary equivalent, divide 5 successively by 2 until the quotient becomes 0. The binary equivalent can be obtained by writing the remainder in each division step from the bottom to the top.
☛ Binary to Decimal
What is the Binary Equivalent of 5 + 27?
5 in binary number system is 101 and 27 is 11011. We can add the binary equivalent of 5 and 27 using binary addition rules [0 + 0 = 0, 0 + 1 = 1, 1 + 1 = 10 note that 1 is a carry over to the next bit]. Therefore, (101)₂ + (11011)₂ = (100000)₂ which is nothing but 32.
☛ Binary to Decimal Calculator
Find the Value of 7 × 5 in Binary Form.
We know that 5 in binary is 101 and 7 is 111. Using the binary multiplication rules (0 × 0 = 0; 0 × 1 = 0 ; 1 × 0 = 0 and 1 × 1 = 1), we can multiply 101 × 111 = 100011 which is 35 in the decimal number system. [5 × 7 = 35]
How Many Bits Does 5 in Binary Have?
We can count the number of zeros and ones to see how many bits are used to represent 5 in binary i.e. 101. Therefore, we have used 3 bits to represent 5 in binary.
How to Convert 5 to Binary Equivalent?
We can divide 5 by 2 and continue the division till we get 0. Note down the remainder in each step.
- 5 mod 2 = 1 - LSB (Least Significant Bit)
- 2 mod 2 = 0
- 1 mod 2 = 1 - MSB (Most Significant Bit)
Write the remainders from MSB to LSB. Therefore, the decimal number 5 in binary can be represented as 101.
☛ Also Check:
- 123 in Binary - 1111011
- 1101 in Binary - 10001001101
- 99 in Binary - 1100011
- 162 in Binary - 10100010
- 3 in Binary - 11
- 48 in Binary - 110000
- 23 in Binary - 10111