Convert 76428 to its binary equivalent.
35. Describe how to convert a binary number to its hexadecimal equivalent.
36. Convert 11000111012 to its hexadecimal equivalent.
37. Describe how to convert a hexadecimal number to its binary equivalent.
38. Convert CD5316 to its binary equivalent.
39. What is binary encoding?
40. Describe the ASCII code.
41. What is extended ASCII?
42. What is binary coded decimal (BCD)?
43. Derive the BCD equivalent for a decimal number 7654.
44. What is the Gray code?
45. What is a word?
46. Describe the least significant bit and the most significant bit.
47. How many decimals can a two-byte word hold?
48. Describe the difference between signed numbers and unsigned numbers.
49. What are the two methods of expressing negative numbers?
50. Explain the one’s complement method of inverting a positive number to a negative number.
51. Use one’s complement method to express the negative number of 98.
52. Explain the two’s complement method of inverting a positive number to a negative number.
53. Find the two’s complement of +5010.
54. What is a floating-point number?
55. Explain how to use scientific notation to express very large or very small numbers.
Logic Basics and Boolean Algebra
Binary concepts and three basic logic functions are the fundamentals of good logic design. The states of an element are represented in binary because an element exists in only two states. A switch that can be toggled to ON or OFF is an example of binary element. The three basic logic functions are AND, OR, and NOT. There are three commonly used methods for expressing logic circuits: Boolean algebraic expressions, logic gates, and ladder diagrams. This chapter covers essential concepts of binary operations, basic logic functions, Boolean algebraic equations, logic gates, and ladder diagrams. Also, all three forms of logic conversions are explained in detail. The chapter concludes with the construction of state tables that are often used to verify the control logic.
4.1 Binary Operations
Binary operations are those elements that can exist in only one of two predetermined states. This is also known as the binary principle. Two examples of binary devices are a motor, which can have a running or stopped state, and a light switch, which can be in the open or closed state. Because there are only two possible outcomes, this two-state binary concept can be used for making decisions.
Binary symbols are used to translate this two-state logic concept into mathematical expressions. A binary zero (0) is used to represent the absence of a signal or the non-occurrence of an event, such as the de-energized motor or the non-actuated switch. A binary one (1) is used to represent the presence of a signal or the occurrence of an event, such as the energized motor or the activated switch. We would use a “0” to represent an open contact and a “1” to represent a closed contact.
4.1.1Positive Logic Elements
Input switches or contacts can be configured or wired in two types: normally open (NO) and normally closed (NC). In elements of the type NO, they produce a binary logic “1” when they are actuated, and a binary logic “0” when non-actuated (Figure 4.1). These elements of type NO are referred to as positive logic elements because they produce a logic “1” when they are actuated. Table 4.1 lists some typical examples of positive logic elements.
4.1.2Negative Logic Elements
A second element type is labeled NC, normally closed. It produces a binary “0” logic when it is actuated, and a binary “1” logic when non-actuated (Figure 4.2). NC types of elements are called negative logic elements. Table 4.2 lists some example of negative logic elements.
Figure 4.1: Positive (normally open) logic elements
Table 4.1: Positive (NO) input logic elements
| Element | Binary
|
|---|
