oscilloscope wrote:
the fig 2.1 suggests its the other way round. So 1 is infact off , and 0 is on. now unless i have completely had this round the wrong way for years and years. , i always figured that connected / on / making a circuit. "1" etc etc , means "ON" , and open circuit is "OFF".
What's happening here is that the switch is either closed, and connecting the write on the right hand side to ground, or it's open, and letting it float. If that wire was connected to a pull-up resistor or a TTL input, it would get pulled up to Vcc. If you look at the voltage on that wire, you'll see either 0V (logical 0) or 5V (logical 1).
In a real circuit, there will be transistors instead of switches, but they serve the same purpose: effectively connecting one wire to another (yes, yes, I know, but those details don't matter for this explanation). The "on" or "off" of the transistor or switch doesn't represent a logic level in itself; it's the voltage on the wire that does that. Imagine two switches joined together, with their other ends connected to Vcc and 0V respectively. If the first is closed and the second open, the output will be logical 1. If the second is closed and the first open, it will be 0. The relationship between on/off and logic level is different for each switch - trying to look at it that way is only going to confuse you.
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so this next page is abit annoying , as its explaining to me about binary , and the representation of base TEN , there is a rather annoying part which explains the mathematical approach to how base TEN is used for letters i think. ? , i had to sit there and think what is the "little i , j , k." next to the little d , and then it twigged. "decimal" and then...
The 'd' here represents 'digit', and the subscripts are just used to distinguish different ones. It's standard mathematical notation.
This is showing the general case, so it can't use actual digits 0-9, and uses the letter d instead. Each digit can be different, so we can't use the same variable for all of them. One option would be to use a*B^3 + b*B^2 + c*B^1 + d*B^0, but you run out of letters fairly quickly that way. So it's common to use the same letter for all of them, and distinguish them with subscripts. It would be more common (and I think more useful) to number them, with d_0 on the B^0 place, d_1 on the B^1 place, and so on. But i, j, k, l does the job too.