Page 78 - Bebop to The Boolean Boogie An Unconventional Guide to Electronics Fundamentals, Components, and Processes

Alternative Numbering Systems 59
-1

100, (25) 1000, (125) etc.
101, (26) 1001, (126)
102, (27) 1002, (127)

42, (22) 442, (122) 4442, (622)
43, (23) 443, (123) 4443, (623)
445 (24) 444, (124) 4444, (624)

I
1

Figure 7-1 1. Counting in quinary

Binary (Base-2!)
Digital systems are constructed out of logic gates that can only represent
two states; thus, computers are obliged to make use of a number system corn-
prising only ~WQ digits. Base-2 number systems are called binary and use the
digits 0 and 1. As usual, each column in a binary number has a weight derived
from the base, anld each digit is combined with its column’s weight to deter-
mine the final value of the number (Figure 7-12).

5ixteens column
Eights mlumn
- Fours column

Ones column

+
x
x
101 IO, = (1 x 16) + (0 8) + (1 x 4) (1 x 2) + (0 1)
= 22,,
Figure 7-1 2. Combining digits with column weights in binary