Why does the same binary bit pattern have different values under different representation schemes?

"Finally, if we come up for air out of all this mass of details, it’s worth emphasizing that there is no intrinsically “right” way to interpret a binary number. If I show you a bit pattern — say, 11000100 — and ask you what value it represents, you can’t tell me without knowing how to interpret it. If I say, “oh, that’s an unsigned number,” then you’d treat each bit as a digit in a simple base 2 numbering scheme. You’d add 2⁷ + 2⁶ + 2² to get 196, then respond, “ah, then that’s the number 196₁₀.” And you’d be right. But if I say, “oh, that’s a sign-magnitude number,” you’d first look at the leftmost bit, see that it’s a 1, and realize you have a negative number. Then you’d take the remaining seven bits and treat them as digits in a simple base 2 numbering scheme. You’d add 2⁶ + 2² to get 68, and then respond, “ah, then that’s the number −68₁₀.” And you’d be right. But then again, if I say, “oh, that’s a two’s-complement number,” you’d first look at the leftmost bit, see that it’s a 1, and realize you’re dealing with a negative number. What is it the negative of? You’d flip all the bits and add one to find out. This would give you 00111100, which you’d interpret as a base 2 number and get 60₁₀. You’d then respond, “ah, then that’s the number −60₁₀.” And you’d be right. So what does 11000100 represent then? Is it 196, −68, or −60? The answer is any of the three, depending on what representation scheme you’re using. None of the data in computers or information systems has intrinsic meaning: it all has to be interpreted according to the syntactic and semantic rules that we invent. In math and computer science, anything can be made to mean anything: after all, we invent the rules."