Multiplying a binary number by 2 is a straightforward operation achieved by shifting all bits one position to the left.
Understanding Binary Multiplication by 2
The core principle behind this method lies in the positional nature of binary numbers. Each position represents a power of 2. Shifting the bits to the left effectively multiplies the value of each bit by 2, and therefore multiplies the entire number by 2.
The Shifting Method
To multiply a binary number by 2, you simply:
- Shift all bits one position to the left.
- Fill the vacated rightmost bit with a 0.
Example:
Let's illustrate this with examples using the information in the reference:
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Example 1:
- 5 in decimal is 101 in binary.
- 5 * 2 = 10 in decimal.
- Multiplying 101 (binary) by 2: 101 becomes 1010
- 1010 (binary) is equal to 10 in decimal.
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Example 2:
- If we start with 11 (3 in decimal) and want to multiply by 2, we shift 11 one position to the left and add a 0:
- 11 becomes 110
- 110 (binary) is equal to 6 (decimal), which is 3 x 2.
Practical Insights
- Efficiency: The shift method is a computationally efficient way to multiply by 2 in binary, as it avoids complex multiplication circuits.
- Analogy to Decimal System: Think of multiplying a number by 10 in the decimal system. You simply add a '0' to the right end of the number (i.e., shifting one position to the left), which is very similar. The same principle applies here, but instead of base 10 we are dealing with base 2.
Summary
| Decimal Operation | Binary Representation | Binary Shifted Left (Result) | Decimal Result |
|---|---|---|---|
| 5 x 2 | 101 | 1010 | 10 |
| 11 x 2 | 11 | 110 | 6 |
In conclusion, multiplying a binary number by 2 is simply achieved by shifting its bits one position to the left, filling the vacated rightmost bit with a 0.
