Base-2
Standard Binary Numbers are unsigned Base 2 numbers.
Binary digits or bits(0, 1) are also expressed in a positional notation system.
- In Standard Binary Notation (unsigned), each digit represents a power of 2.
- The left-most bit is called the most significant bit or the high order bit and the right-most bit is called the least significant bit or the low order bit.
- In an 8-bit number the column positions have these values:
|
Position Value: |
27 |
26 |
25 |
24 |
23 |
22 |
21 |
20 |
|
Digit Value: |
128s |
64s |
32s |
16s |
8s |
4s |
2s |
1s |
|
Binary Number: |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
1 |
-
So, if interpreted as expressed inStandard Binary Notation,the 8-bit number expresses the highest magnitude an 8-bit pattern can represent because we can only count up to 1 in any column before carrying over to the next digit value
(1x128) + (1x64) + (1x32) + (1x16) + (1x8) + (1x4) + (1x2) + (1x1) = 255.)
- Just as in decimal numbers, 999 (each digit maximized) is exactly one less than the next digit which is 1000, 111111112 above (i.e., 25510) is also exactly 1 less than the digit value of the next column which in this case is 28 or 256.
- In terms of the number of digits needed to represent a value, you only need a maximum of 3 decimal digits to represent a value that may require 8 binary digits.
- It follows then that as we increase the base value from 2, we would require less and less digits to represent the same binary number.
- Since we are particularly interested in powers of 2 numbers, we can observe further relationships with other base values that are powers of 2.