15 in Binary
15 in binary is 1111. 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 4 bits to represent 15 in binary. In this article, let us learn how to convert the decimal number 15 to binary.
How to Convert 15 in Binary?
Step 1: Divide 15 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.
| Dividend | Remainder |
|---|---|
| 15/2 = 7 | 1 |
| 7/2 = 3 | 1 |
| 3/2 = 1 | 1 |
| 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 15.
Therefore, the binary equivalent of decimal number 15 is 1111.
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Let us have a look at the value of the decimal number 15 in the different number systems.
- 15 in Binary: 15₁₀ = 1111₂
- 15 in Octal: 15₁₀ = 17₈
- 15 in Hexadecimal: 15₁₀ = F₁₆
- 1111₂ in Decimal: 15₁₀
Problem Statements:
| What is 15 in Binary? - (Base 2) | (1111)₂ |
| What is 15 in Hexadecimal? - (Base 16) | (F)₁₆ |
| What is 15 in Octal? - (Base 8) | (17)₈ |
| Cube Root of 15 | 2.466212 |
| Is 15 a Perfect Cube? | No |
| Is 15 a Composite Number? | Yes |
| Is 15 a Perfect Square? | No |
| Is 15 a Prime Number? | No |
| Square Root of 15 | 3.872983 |
FAQs on 15 in Binary
What is 15 in Binary?
15 in binary is 1111. To find decimal to binary equivalent, divide 15 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.
How to Convert 15 to Binary Equivalent?
We can divide 15 by 2 and continue the division till we get 0. Note down the remainder in each step.
- 15 mod 2 = 1 - LSB (Least Significant Bit)
- 7 mod 2 = 1
- 3 mod 2 = 1
- 1 mod 2 = 1 - MSB (Most Significant Bit)
Write the remainders from MSB to LSB. Therefore, the decimal number 15 in binary can be represented as 1111.
Find the Value of 7 × 15 in Binary Form.
We know that 15 in binary is 1111 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 1111 × 111 = 1101001 which is 105 in the decimal number system. [15 × 7 = 105]
What is the Binary Equivalent of 15 + 24?
15 in binary number system is 1111 and 24 is 11000. We can add the binary equivalent of 15 and 24 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, (1111)₂ + (11000)₂ = (100111)₂ which is nothing but 39.
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How Many Bits Does 15 in Binary Have?
We can count the number of zeros and ones to see how many bits are used to represent 15 in binary i.e. 1111. Therefore, we have used 4 bits to represent 15 in binary.
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