What is 10011010 in decimal?
154
Converting Binary 10011010 to Decimal
To convert a binary number to its decimal equivalent, we multiply each digit by the corresponding power of 2, starting from the rightmost digit (which corresponds to $2^0$) and moving leftwards. The sum of these products gives the decimal value.
Let's take the binary number 10011010.
We can list the digits and their corresponding powers of 2 from right to left:
- The rightmost digit is 0, which corresponds to $2^0 = 1$.
- The next digit is 1, which corresponds to $2^1 = 2$.
- The next digit is 0, which corresponds to $2^2 = 4$.
- The next digit is 1, which corresponds to $2^3 = 8$.
- The next digit is 1, which corresponds to $2^4 = 16$.
- The next digit is 0, which corresponds to $2^5 = 32$.
- The next digit is 0, which corresponds to $2^6 = 64$.
- The leftmost digit is 1, which corresponds to $2^7 = 128$.
Now, we multiply each binary digit by its corresponding power of 2 and sum the results:
| Binary Digit | Position (from right, starting at 0) | Power of 2 ($2^{\text{Position}}$) | Product (Digit $\times$ Power of 2) |
|---|---|---|---|
| 1 | 7 | $2^7 = 128$ | $1 \times 128 = 128$ |
| 0 | 6 | $2^6 = 64$ | $0 \times 64 = 0$ |
| 0 | 5 | $2^5 = 32$ | $0 \times 32 = 0$ |
| 1 | 4 | $2^4 = 16$ | $1 \times 16 = 16$ |
| 1 | 3 | $2^3 = 8$ | $1 \times 8 = 8$ |
| 0 | 2 | $2^2 = 4$ | $0 \times 4 = 0$ |
| 1 | 1 | $2^1 = 2$ | $1 \times 2 = 2$ |
| 0 | 0 | $2^0 = 1$ | $0 \times 1 = 0$ |
Summing the products:
$128 + 0 + 0 + 16 + 8 + 0 + 2 + 0 = 154$
Therefore, the decimal equivalent of the binary number 10011010 is 154.
Important Questions from Binary to Decimal Conversion
What is the binary number equivalent to decimal number 1011 ?
If (1012)3 = (112)R the value of the radix ‘R’ is
What would be the equivalent binary expression for 456?
Decimal equivalent of Binary No. 100 is:
Decimal fraction 0.375 in binary form is
