Answer:
10101010 = 170
(Excess-M binary number) = 167
Explanation:
If you want to learn about excess-M binary numbers, you're in luck! I'm here to explain them to you in a fun and easy way. Excess-M binary numbers are a clever trick to store positive and negative numbers using only 0s and 1s. M is a magic number that we choose to make this work. M is the number that we use to represent 0 in this system. To get any other number, we just add M to it and write it in binary. For example, let's say M is 7. Then 0 is 7 + 0 = 7, which is 0111 in binary. And -3 is 7 + (-3) = 4, which is 0100 in binary.
But how do we go back from binary to base 10? Easy peasy! We just do the opposite of what we did before. We take the binary number and convert it to decimal using some simple math. Then we subtract M from it and voila! We have our base 10 number. For example, let's take 10101010 in excess-3. First, we convert it to decimal by multiplying each bit by its place value, starting from the right:
10101010 = (0 * 2^0) + (1 * 2^1) + (0 * 2^2) + (1 * 2^3) + (0 * 2^4) + (1 * 2^5) + (0 * 2^6) + (1 * 2^7)
10101010 = (0 * 1) + (1 * 2) + (0 * 4) + (1 * 8) + (0 * 16) + (1 * 32) + (0 * 64) + (1 * 128)
10101010 = 0 + 2 + 0 + 8 + 0 + 32 + 0 + 128
10101010 = 170
Then we subtract M, which is 3, from this decimal value:
170 - 3 = 167
So the base 10 value of the excess-3 binary number 10101010 is 167.
Pretty cool, huh? Now you know how to use excess-M binary numbers like a pro!
Footnotes:
The first bit in a binary number is worth 128 if it's a one (the zero doesn't count). The second bit is worth 64, the third bit is worth 32, the fourth bit is worth 16, the fifth bit is worth 8, the sixth bit is worth 4, the seventh bit is worth 2, and the eighth bit is worth one.