Question

Convert the following to decimal:
a. 1011110111000.....0
b. 010000101101001101000.....0

Answer 1

To convert the given binary numbers to decimal, each digit representing a '1' in the binary number is associated with a power of two, starting from 2^0 on the rightmost digit and doubling as we move left. We sum up the values of these positions to get the decimal equivalent.

Step-by-step explanation:

To convert the given binary numbers to decimal, we need to understand that each digit in a binary number represents a power of two, with the least significant digit (rightmost) being the power zero. We'll add up the value of each digit where there's a '1'.

For example, let's convert the binary number 1011110111000 to decimal:

• The rightmost digit is worth 1 (20).
• Going left, the next digit is worth 2 (21).
• This continues, doubling each time until we reach the leftmost '1'.
• We sum the values of all positions with a '1'.

Another example: For the binary number 010000101101001101000, we would apply the same process, summing the powers of two corresponding to the positions of the '1's.