convert 1.1 base five to a binary number
To convert a number from base five to binary, we need to convert it to base ten first and then convert it to binary.
To convert 1.1 from base five to base ten, we can use the formula:
(1 * 5^0) + (1 * 5^-1) = 1.2 base ten
Now, let's convert 1.2 base ten to binary.
To convert a decimal number to binary, we can multiply the decimal part by 2 repeatedly and keep track of the carryover until the decimal part becomes 0 or until we get the desired level of precision.
1.2 * 2 = 2.4 (take integer part: 1, carryover: 0)
0.4 * 2 = 0.8 (take integer part: 0, carryover: 0)
0.8 * 2 = 1.6 (take integer part: 1, carryover: 0)
0.6 * 2 = 1.2 (take integer part: 1, carryover: 0)
0.2 * 2 = 0.4 (take integer part: 0, carryover: 0)
0.4 * 2 = 0.8 (take integer part: 0, carryover: 0)
0.8 * 2 = 1.6 (take integer part: 1, carryover: 0)
0.6 * 2 = 1.2 (take integer part: 1, carryover: 0)
The decimal part repetitively yields 1, 0, 1, 1, 0, 0, 1, 1...
Therefore, 1.1 base five is approximately equal to 1.10110011... base two.
To convert 1.1 from base five to binary, we first need to convert it to base 10 and then convert it to binary.
Step 1: Convert from base five to base 10:
1.1 base five can be written as (1 * (5^0)) + (1 * (5^-1)).
Calculating the value, we get:
(1 * 1) + (1 * (1/5)) = 1 + 0.2 = 1.2.
Step 2: Convert from base 10 to binary:
To convert 1.2 from base 10 to binary, we will use the following steps:
- Multiply the number by 2.
- Write down the integer part of the result.
- Take the fractional part of the result.
- Repeat the process with the fractional part until the fractional part becomes zero or until you get the desired accuracy.
Here's how we apply this process:
1.2 * 2 = 2.4
Integer part = 2
Fractional part = 0.4
0.4 * 2 = 0.8
Integer part = 0
Fractional part = 0.8
0.8 * 2 = 1.6
Integer part = 1
Fractional part = 0.6
0.6 * 2 = 1.2
Integer part = 1
Fractional part = 0.2
0.2 * 2 = 0.4
Integer part = 0
Fractional part = 0.4
As the fractional part (0.4) is repeating and we do not want an infinite decimal representation, we can stop here.
So, 1.1 base five is approximately equal to 10.0011 in binary.
To convert a number from base five to binary, you need to do the following steps:
1. Break down the number into its individual digits. In this case, the number is 1.1 in base five, which means there is a whole number part (1) and a fractional part (0.1).
2. Convert each digit to its binary equivalent. In base five, there are only five possible digits: 0, 1, 2, 3, and 4. To convert these digits to binary:
- 0 in base five is 0 in binary: 0 (base 5) = 0 (base 2)
- 1 in base five is 1 in binary: 1 (base 5) = 1 (base 2)
- 2 in base five is 10 in binary: 2 (base 5) = 10 (base 2)
- 3 in base five is 11 in binary: 3 (base 5) = 11 (base 2)
- 4 in base five is 100 in binary: 4 (base 5) = 100 (base 2)
3. Convert the whole number part to binary. In this case, the whole number part is 1, which remains the same in binary: 1 (base 5) = 1 (base 2).
4. Convert the fractional part to binary. In this case, the fractional part is 0.1. To do this, multiply the fractional part by the base (five) and keep the whole number part of the result. Repeat this process until the fractional part becomes 0 or until you have achieved the desired level of precision. Here is the calculation:
- 0.1 (base 5) * 5 (base 10) = 0.5 (base 10)
- The whole number part is 0 (base 10), so the next multiplication is:
- 0.5 (base 10) * 5 (base 10) = 2.5 (base 10)
- The whole number part is 2 (base 10), so the next multiplication is:
- 0.5 (base 10) * 5 (base 10) = 2.5 (base 10)
- The whole number part is 2 (base 10), and since we have reached the desired level of precision (1 digit after the decimal point), we stop here.
The binary representation of 0.1 (base 5) is 0.2 (base 10).
5. Combine the whole number and fractional parts in binary. In this case, the whole number part is 1 (base 5) = 1 (base 2), and the fractional part is 0.2 (base 10) = 0.001100110011... (base 2) (repeating pattern).
Combining them gives us: 1.1 (base 5) = 1.001100110011... (base 2).
Therefore, the binary representation of 1.1 (base 5) is 1.001100110011... (base 2) (repeating pattern).