127 in Binary
127 in binary is 1111111. 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 7 bits to represent 127 in binary. In this article, let us learn how to convert the decimal number 127 to binary.
How to Convert 127 in Binary?
Step 1: Divide 127 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 |
|---|---|
| 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 127.
Therefore, the binary equivalent of decimal number 127 is 1111111.
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Let us have a look at the value of the decimal number 127 in the different number systems.
- 127 in Binary: 127₁₀ = 1111111₂
- 127 in Octal: 127₁₀ = 177₈
- 127 in Hexadecimal: 127₁₀ = 7F₁₆
- 1111111₂ in Decimal: 127₁₀
Problem Statements:
| What is 127 in Binary? - (Base 2) | (1111111)₂ |
| What is 127 in Hexadecimal? - (Base 16) | (7F)₁₆ |
| What is 127 in Octal? - (Base 8) | (177)₈ |
| Cube Root of 127 | 5.026526 |
| Is 127 a Composite Number? | No |
| Square Root of 127 | 11.269428 |
| Is 127 a Perfect Cube? | No |
| Is 127 a Perfect Square? | No |
| Is 127 a Prime Number? | Yes |
FAQs on 127 in Binary
What is 127 in Binary?
127 in binary is 1111111. To find decimal to binary equivalent, divide 127 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 127 to Binary Equivalent?
We can divide 127 by 2 and continue the division till we get 0. Note down the remainder in each step.
- 127 mod 2 = 1 - LSB (Least Significant Bit)
- 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 127 in binary can be represented as 1111111.
Find the Value of 3 × 127 in Binary Form.
We know that 127 in binary is 1111111 and 3 is 11. Using the binary multiplication rules (0 × 0 = 0; 0 × 1 = 0 ; 1 × 0 = 0 and 1 × 1 = 1), we can multiply 1111111 × 11 = 101111101 which is 381 in the decimal number system. [127 × 3 = 381]
What is the Binary Equivalent of 127 + 51?
127 in binary number system is 1111111 and 51 is 110011. We can add the binary equivalent of 127 and 51 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, (1111111)₂ + (110011)₂ = (10110010)₂ which is nothing but 178.
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How Many Bits Does 127 in Binary Have?
We can count the number of zeros and ones to see how many bits are used to represent 127 in binary i.e. 1111111. Therefore, we have used 7 bits to represent 127 in binary.
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