(b) Binary counting. Figure 1-4 lists the first 20 binary numbers. While the same positional
notation system is used, the decimal system uses powers of 10, and the binary system uses powers of 2.
The number 125 actually means (1x102) + (2x101) + (5x100). In the binary system, the same number
(125) is represented as 1111101, meaning (1x26) + (1x25) + (1x24) + (1x23) + (1x22) + (0x21) + (1x20).
(3) Conversion by Table. A table must have the required range of numbers that are to be
converted. Such a table can be constructed to any desired length. When you make a binary table you
must use the power of 2 (Figure 1-4). Using Figure 1-4 you can convert decimal numbers from 0 to 20.
To represent the decimal value of 0, all positions of the binary coefficients would be 0. To represent the
decimal value of 1,023, all positions of the binary coefficients would be 1. In Figure 1-3 the example of
the binary coefficients equals a 2510. The process of conversion is shown below: