Page 853 - Mechanical Engineers' Handbook (Volume 2)

844 Mechatronics

2.3 Other Common Op Amp Circuits
Some other useful op amp circuits are described in Fig. 29 (page 843).

3 BINARY NUMBERS
Computers and digital electronics used in mechatronic systems are described by binary ar-
ithmetic. Therefore, it is important to understand binary numbers to fully understand the
function of computers. First, consider a base-10 number as in standard mathematics. Base-
10 numbers have 10 possible digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). Consider a number such as
234. Here the 4 represents the 1’s digit, the 3 represents the 10’s digit, and the 2 represents
the 100’s digit. The number 234 represents four 1’s and three 10’s and two 100’s(4 * 1
3 * 10 2 * 100 234). The value of each digit increases by a factor of 10 as you move
to the left and decreases by a factor of 10 as you move to the right. Consider a number such
as 234:
2 3 4
1’s digit
10’s digit
100’s digit

4 represents the sum of nine 1’s
3 represents the sum of seven 10’s
2 represents the sum of one 100
Now, consider a base-2 number, or a binary number. Base-2 numbers have two possible
digits (0, 1). Again, consider the number 234. With binary numbers the value of each digit
increases by a factor of 2 as you move to the left and decreases by a factor of 2 as you
move to the right. To write this number as a binary number requires zero 1’s and one 2’s
and zero 4’s and one 8’s and zero 16’s and one 32’s and one 64’s and one 128’s (234
11101010 0 * 1 1 * 3 0 * 4 1 * 8 0 * 16 1 * 32 1 * 64 1 * 128):
Binary base 2: two possible digits (0, 1)

234 11101010

0 1’s
1 2’s
0 4’s
1 8’s
0 16’s
1 32’s
1 64’s
1 128’s

3.1 Binary Numbers of Different Size
Each digit in a binary number (either a 0 or a 1) is called a bit—‘‘binary digit.’’ A nibble
is a group of 4 bits, a byte is a group of 8 bits, a word is a group of 16 bits, and a double
word (dword) is a group of 32 bits. Each bit is numbered starting with zero and moving to