Convert the number 96 to its binary equivalent.
The Correct Answer and Explanation is :
The binary equivalent of the decimal number 96 is 1100000.
Explanation:
To convert the decimal number 96 to its binary equivalent, follow these steps:
Step 1: Divide the Number by 2
We continuously divide 96 by 2, keeping track of the quotient and remainder.
| Division | Quotient | Remainder |
|---|---|---|
| 96 ÷ 2 | 48 | 0 |
| 48 ÷ 2 | 24 | 0 |
| 24 ÷ 2 | 12 | 0 |
| 12 ÷ 2 | 6 | 0 |
| 6 ÷ 2 | 3 | 0 |
| 3 ÷ 2 | 1 | 1 |
| 1 ÷ 2 | 0 | 1 |
Step 2: Read the Remainders in Reverse Order
When we read the remainders from bottom to top, we get:
1100000
Thus, the decimal number 96 in binary is 1100000₂.
Understanding the Concept:
- The binary number system uses only two digits: 0 and 1.
- Every digit in a binary number represents a power of 2, just as in the decimal system, each digit represents a power of 10.
- For example, 1100000₂ can be expanded as: [
(1 \times 2^6) + (1 \times 2^5) + (0 \times 2^4) + (0 \times 2^3) + (0 \times 2^2) + (0 \times 2^1) + (0 \times 2^0)
] [
64 + 32 + 0 + 0 + 0 + 0 + 0 = 96
]
Thus, 96 = 1100000₂, confirming the correctness of our conversion.
Now, I’ll generate an image representing this binary conversion.
Here is the image illustrating the conversion of the decimal number 96 to its binary equivalent (1100000) with step-by-step calculations. Let me know if you need any modifications or further explanations!
