Page 80 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Alternative Numbering Systems 6 7

I
7 v

1000, (8) 10000, (16) etc.
1001, (9) 10001, (17)
1010, (IO) 10010, (18)

1101, (13) 11101, (29)
1110, (14) 11110, (30)
1111, (15) 11111, (31)

Figure 7-1 3. Counting in binary

Octal (Base-$) and Hexadecimal (Base-1 6)
Any number system having a base that is a power of two (2,4,8, 16,32,
etc.) can be easily mapped into its binary equivalent and vice versa. For this
reason, electronics engineers typically make use of either the octal (base-8)
or hexadecimal (base-16) systems.
As a base-8 system, octal requires eight individual symbols to represent all
of its digits. This isn’t a problem because we can simply use the symbols 0 through
7 that we know and love so well. However, as a base-16 system, hexadecimal
requires sixteen individual symbols to represent all of its digits. This does pose
something of a problem because there are only ten Hindu-Arabic symbols
available (0 through 9). One solution would be to create some new symbols,
but some doubting Thomases (and Thomasinas) regard this as less than optimal
because it would necessitate the modification of existing typewriters and com-
puter keyboards. PLS an alternative, the first six letters of the alphabet are
brought into play l(Figure 7-14).

Hexadecimal 0 1 2 3 4 5 6 7 8 9 A 6 C D E F
Decimal 0 1 2 3 4 5 6 7 8 9 10 I1 I2131415

Figure 7-3 4. The sixteen hexadecimal digits