BINARY NUMBERS
First lets look at our decimal number system --we use 10 digits (0 thru 9)
In the number 1247 we have 1 x 1000=1000 Each numbers place tells its value
+ 2 x 100 = 200
+ 4 x 10 = 40 We multiply the number times its
+ 7 x 1 = 7 value to get the total value and add
1247 them together
So the value of a decimal number really uses powers of 10 like this
103 102 101 100 Each number (because of its position) tells us
1 2 4 7 what power of 10 we use to multiply it by.
The binary number system uses two digits (0 & 1) and it works the same way.
But binary uses powers
of 2!
The position of the digit (0 or 1) tells which value (power of 2) you multiply by.
23 22 21 20
So the binary number 1 0 1 1 becomes 1 x 8 (23) = 8
0 x 4 (22) =
0
1 x 2 (21) = 2
1
x 1 (20) = 1
and
has a decimal value = 11
27 26 25 24 23 22 21
20
so
what about the binary number 1 0
1 1 0
0 1 1
just multiply the value above the digit
by the digit (0 or 1)and add. so we have 1 x 128 (27) = 128
0 x 64 (26) = 0
1 x 32 (25) = 32
1 x 16 (24) = 16
0 x 8 (23) = 0
0 x 4 (22) = 0
1 x 2 (21) = 2
1 x
1 (20) = 1
decimal
value = 179
How about the binary number 1
0 0 0
0 0 0 1
Don’t add the 0 positions— just the places where there is
a 1, right?
Now try the binary number 0 0 0 1 1 1 1 1
Notice that if you start on the right hand
end, the place value doubles moving left
128 64
32 16 8
4 2 1
just add them up!
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