Method:
- Write down the 8-bit binary number: Make sure you have all 8 digits present, representing the number from the leftmost bit (most significant bit) to the rightmost bit (least significant bit).
- Assign powers of 2 to each bit position: Write down the powers of 2 next to each binary digit, starting with 2^7 for the leftmost bit and decreasing by 1 for each position to the right. So, for an 8-bit number, your powers will be 2^7, 2^6, 2^5, ..., 2^0.
- Multiply each digit by its corresponding power of 2: This step involves multiplying each binary digit (0 or 1) by its corresponding power of 2. If the digit is 0, the product will be 0. If the digit is 1, the product will be the value of the power of 2.
- Add up the products from step 3: Sum all the products you obtained in the previous step. This final sum will be the denary equivalent of your 8-bit binary number.
Example:
Let's convert the binary number 10101110 to denary:
Binary number: 1 0 1 0 1 1 1 0
put binary digits in the correct place beneath each power of 2
Powers of 2:
27 26 25 24 23 22 21 20
128 64 32 16 8 4 2 1
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1 0 1 0 1 1 1 0
Sum: 128 + 32 + 8 + 4 + 2 = 174
Therefore, the denary equivalent of the binary number 10101110 is 174.
Additional Tips:
You can use a table to organize the calculations, listing the binary digits, powers of 2.
