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
Let * be binary operation defined on R by \(\rm p * q=\frac{p+q}{2}, \forall \) p, q ∈ R. The operation is:
Convert 29 into binary.
A. 10101
B. 11110
C. 11101
D. 11001
The product of the two binary numbers 011 and 110 is:
Consider the equation (43)x = (y3)8 where x and y are unknown. The number of possible solution is
P, Q, and R are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1’s complement, and 2’s complement representations, respectively. The 6-bit 2’s complement representation of (P + Q + R) is
