13 in Binary
13 in binary is 1101. 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 13 in binary. In this article, let us learn how to convert the decimal number 13 to binary.
How to Convert 13 in Binary?
Step 1: Divide 13 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 |
|---|---|
| 13/2 = 6 | 1 |
| 6/2 = 3 | 0 |
| 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 13.
Therefore, the binary equivalent of decimal number 13 is 1101.
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Let us have a look at the value of the decimal number 13 in the different number systems.
- 13 in Binary: 13₁₀ = 1101₂
- 13 in Octal: 13₁₀ = 15₈
- 13 in Hexadecimal: 13₁₀ = D₁₆
- 1101₂ in Decimal: 13₁₀
Problem Statements:
| What is 13 in Binary? - (Base 2) | (1101)₂ |
| What is 13 in Hexadecimal? - (Base 16) | (D)₁₆ |
| What is 13 in Octal? - (Base 8) | (15)₈ |
| Is 13 a Prime Number? | Yes |
| Is 13 a Perfect Square? | No |
| Cube Root of 13 | 2.351335 |
| Is 13 a Composite Number? | No |
| Is 13 a Perfect Cube? | No |
| Square Root of 13 | 3.605551 |
FAQs on 13 in Binary
What is 13 in Binary?
13 in binary is 1101. To find decimal to binary equivalent, divide 13 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 13 to Binary Equivalent?
We can divide 13 by 2 and continue the division till we get 0. Note down the remainder in each step.
- 13 mod 2 = 1 - LSB (Least Significant Bit)
- 6 mod 2 = 0
- 3 mod 2 = 1
- 1 mod 2 = 1 - MSB (Most Significant Bit)
Write the remainders from MSB to LSB. Therefore, the decimal number 13 in binary can be represented as 1101.
Find the Value of 10 × 13 in Binary Form.
We know that 13 in binary is 1101 and 10 is 1010. Using the binary multiplication rules (0 × 0 = 0; 0 × 1 = 0 ; 1 × 0 = 0 and 1 × 1 = 1), we can multiply 1101 × 1010 = 10000010 which is 130 in the decimal number system. [13 × 10 = 130]
What is the Binary Equivalent of 13 + 94?
13 in binary number system is 1101 and 94 is 1011110. We can add the binary equivalent of 13 and 94 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, (1101)₂ + (1011110)₂ = (1101011)₂ which is nothing but 107.
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How Many Bits Does 13 in Binary Have?
We can count the number of zeros and ones to see how many bits are used to represent 13 in binary i.e. 1101. Therefore, we have used 4 bits to represent 13 in binary.
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- 2000 in Binary - 11111010000
- 123 in Binary - 1111011