1023 in Binary
1023 in binary is 1111111111. 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 10 bits to represent 1023 in binary. In this article, we will show how to convert the decimal number 1023 to binary.
- 1023 in Binary: 1023₁₀ = 1111111111₂
- 1023 in Octal: 1023₁₀ = 1777₈
- 1023 in Hexadecimal: 1023₁₀ = 3FF₁₆
- 1111111111₂ in Decimal: 1023₁₀
How to Convert 1023 in Binary?
Step 1: Divide 1023 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 |
|---|---|
| 1023/2 = 511 | 1 |
| 511/2 = 255 | 1 |
| 255/2 = 127 | 1 |
| 127/2 = 63 | 1 |
| 63/2 = 31 | 1 |
| 31/2 = 15 | 1 |
| 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 1023.
Therefore, the binary equivalent of decimal number 1023 is 1111111111.
☛ Decimal to Binary Calculator
Problem Statements:
| What is 1023 in Binary? - (Base 2) | (1111111111)₂ |
| What is 1023 in Hexadecimal? - (Base 16) | (3FF)₁₆ |
| What is 1023 in Octal? - (Base 8) | (1777)₈ |
| Is 1023 a Prime Number? | No |
| Cube Root of 1023 | 10.076086 |
| Is 1023 a Perfect Square? | No |
| Square Root of 1023 | 31.984371 |
| Is 1023 a Perfect Cube? | No |
| Is 1023 a Composite Number? | Yes |
FAQs on 1023 in Binary
What is 1023 in Binary?
1023 in binary is 1111111111. To find decimal to binary equivalent, divide 1023 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 1023 to Binary Equivalent?
We can divide 1023 by 2 and continue the division till we get 0. Note down the remainder in each step.
- 1023 mod 2 = 1 - LSB (Least Significant Bit)
- 511 mod 2 = 1
- 255 mod 2 = 1
- 127 mod 2 = 1
- 63 mod 2 = 1
- 31 mod 2 = 1
- 15 mod 2 = 1
- 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 1023 in binary can be represented as 1111111111.
Find the Value of 8 × 1023 in Binary Form.
We know that 1023 in binary is 1111111111 and 8 is 1000. Using the binary multiplication rules (0 × 0 = 0; 0 × 1 = 0 ; 1 × 0 = 0 and 1 × 1 = 1), we can multiply 1111111111 × 1000 = 1111111111000 which is 8184 in the decimal number system. [1023 × 8 = 8184]
How Many Bits Does 1023 in Binary Have?
We can count the number of zeros and ones to see how many bits are used to represent 1023 in binary i.e. 1111111111. Therefore, we have used 10 bits to represent 1023 in binary.
What is the Binary Equivalent of 1023 + 3?
1023 in binary number system is 1111111111 and 3 is 11. We can add the binary equivalent of 1023 and 3 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, (1111111111)₂ + (11)₂ = (10000000010)₂ which is nothing but 1026.
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- 38 in Binary - 100110