The binary equivalent of (234.125)10?
(11101010.001)2
Understanding Decimal to Binary Conversion
This question requires converting a decimal number, specifically (234.125)10, into its binary (base-2) equivalent. The process involves converting the integer part and the fractional part separately.
Converting the Integer Part: (234)10
We use the method of successive division by 2 for the integer part:
| Division | Quotient | Remainder |
| $234 \div 2$ | $117$ | $0$ |
| $117 \div 2$ | $58$ | $1$ |
| $58 \div 2$ | $29$ | $0$ |
| $29 \div 2$ | $14$ | $1$ |
| $14 \div 2$ | $7$ | $0$ |
| $7 \div 2$ | $3$ | $1$ |
| $3 \div 2$ | $1$ | $1$ |
| $1 \div 2$ | $0$ | $1$ |
Reading the remainders from bottom to top, we get the binary equivalent of the integer part: (11101010)2.
Converting the Fractional Part: (0.125)10
For the fractional part, we use the method of successive multiplication by 2:
- $0.125 \times 2 = 0.250$. The integer part is $0$.
- $0.250 \times 2 = 0.500$. The integer part is $0$.
- $0.500 \times 2 = 1.000$. The integer part is $1$.
Reading the integer parts from top to bottom, we get the binary equivalent of the fractional part: (0.001)2.
Combining Integer and Fractional Parts
Combining the binary results for the integer and fractional parts, we get:
(234.125)10 = (11101010)2 + (0.001)2 = (11101010.001)2
Final Answer Comparison
Comparing this result with the given options:
- Option 1: (11101010.101)2
- Option 2: (10101010.011)2
- Option 3: (11101010.001)2
- Option 4: (10101110.011)2
The calculated binary equivalent matches Option 3.
Important Questions from Binary Operations
What is the binary equivalent of the decimal number 0.3125?
What is (1000000001) 2– (0.0101) 2equal to?
The decimal number (127.25) 10, when converted to binary number, takes the form
If (11101011) 2is converted to decimal system, then the resulting number is
If the number 235 in decimal system is converted into binary system, then what is the resulting number?
