6.1 DIGITAL BUILDING BLOCKS 271
6.1 Digital Building Blocks
The primary advantage of digital technology is the low cost, simplicity, and versatility of the
digital building blocks. Because digital signals have a finite number of discrete amplitudes at any
given time, distinctive digital building blocks are developed to process them. Digital systems are
built by repeating a very few simple blocks. The approach becomes very powerful because the
blocks (mass-produced in enormous numbers) are inexpensive in IC form and can be repeated
thousands of times.
The two-state nature of digital technology makes the binary number system its natural tool.
In a binary system there are only two digits, namely, 0 and 1. The vast majority of present digital
computers use the binary system, which has two binary digits (bits), 0 and 1. Internal representation
of information in a digital computer is in groups of bits. Besides the binary system (base 2), in
the digital world, the most commonly used number systems are octal (base 8) and hexadecimal
(base 16).
EXAMPLE 6.1.1
A signal stands for 0110 with positive logic in which low stands for 0 and high stands for 1. If
negative logic (in which low stands for 1 and high stands for 0) is used, what digits are represented
by the signal?
Solution
The signal sequence reads: low–high–high–low. With negative logic, the signal stands for 1001.
EXAMPLE 6.1.2
If the time occupied in transmitting each binary digit is 1μs, find the rate of information
transmission if 1 baud is equal to 1 bit per second (bit/s).
Solution
Since the time per digit is 1× 10 −^6 s, one can transmit 10^6 digits per second. The information
rate is then 1× 106 bits, or 1 megabaud (M baud). Note that speeds of over 100 M baud are quite
possible.
Number Systems
A number system, in general, is an ordered set of symbols (digits) with relationships defined for
addition, subtraction, multiplication, and division. The base (radix) of the number system is the
total number of digits in the system. For example, in our decimal system, the set of digits is{0, 1,
2, 3, 4, 5, 6, 7, 8, 9}and hence the base (radix) is ten (10); in the binary system, the set of digits
(bits) is{0, 1}and hence the base or radix is two (2).
There are two possible ways of writing a number in a given system: positional notation and
polynomial representation. For example, the number 2536.47 in our decimal system is represented
in positional notation as (2536.47) 10 , whereas in polynomial form it is 2× 103 + 5 × 102 + 3 ×
