Owner`s manual

NexSys
®
Modules
Here is the decimal example described:
10 = (1*ten) + (0*one) = ten
Likewise, other decimal values:
35
= (3*10) + (5*1)
= 30 + 5
= 35
528
= (5*100) + (2*10) + (8*1)
= 500 + 20 + 8
= 528
2046
= (2*1000) + (0*100) + (4*10) + (6*1)
= 2000 + 000 + 40 + 6
= 2046
However, since this is really only converting decimal back into decimal, it is of limited
usefulness. Retaining the above concepts and applying it to the other numbering
systems makes things much more clear. Looking at Base-2, digits are in very short
supply. Counting from zero, one has “0,” “1,” and then one must start again. Add a
placeholder, and again the result is “10.” However, now “10” represents two, not ten.
The “1” in “10” binary has a value of two times the place to its right, and the place
to it’s right has a one’s value.
Analyzing this example with the approach used above:
10 = (1*two) + (0*one) = two
It becomes readily apparent that “10” does not always represent “ten,” it is entirely
dependent on the base of the numbering system being used. Other binary values:
100011 b
= (1*32) + (0*16) + (0*8) + (0*4) + (1*2) + (1*1)
= 32 + 0 + 0 + 0 + 2 + 1
= 35
1000010000 b
= (1*512) + (0*256) + (0*128) + (0*64) + (0*32) + (1*16) + (0*8) + (0*4)
+ (0*2) + (0*1)
= 512 + 0 + 0 + 0 + 0 + 16 + 0 + 0 + 0 + 0
= 528
11111111110 b
= (1*1024) + (1*512) + (1*256) + (1*128) + (1*64) + (1*32) + (1*16) + (1*8)
+ (1*4) + (1*2) + (0*1)
= 1024 + 512 + 256 + 128 + 64 + 32 + 16 + 8 + 4 + 2 + 0
= 2046