(A) a basic digital logic

1. Digital systems: binary discrete information processing systems

2. Number and number conversion system

Binary notation: binary counting method with

1. Decimal (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
2. Binary (0, 1)
3. Octal (0, 1, 2, 3, 4, 5, 6, 7)
4. Hex (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F)

Numeric conversion

1. n hexadecimal to decimal: Press the right expansion method
2. Decimal to binary n: integer part even multiplication (modulo n addition to reverse write), the fractional part even multiplication (called n rounded sequential write)

Binary arithmetic operations

1. Binary addition:
   (1) 0 + 0 = 00
   (2) 0 + 1 = 01
   (3) 0 + 1 = 01
   (4) 1 + 1 = 10
2. Binary subtraction
   (1) 00 = 00
   (2) 1 - 1 = 00
   (3) 10 = 10
   (4) 10--1 = 1
3. Binary multiplication
   (1) = 0 * 0 0
   (2) 0 * 1 = 0
   (3) 1 * 0 = 0
   (4) 1 * 1 = 1
4. Calculated complement
   (1) a positive number equal to the complement of the original code
   (2) is equal to the original negative complement code plus a negated

3. two - coded decimal (BCD code): with 4-bit binary code to represent a decimal number

You have the right code:

1. 8421 yards
2. 5421 yards
3. 2421 yards

No right code:

1. 3 code (corresponding to 8421 yards plus 3 decimal or binary 0011)
2. Gray code (cyclic code): Only one difference between two adjacent codes, the rest of you are the same
3. Relationship between bit Gray code G [2] G [1] G [0] and the 3-bit binary code B [2] B [1] B [0] is:
   (. 1) G [2] = B [2]
   ( 2) G [. 1] = B [2] ^ B [. 1]
   (. 3) G [0] = B [. 1] ^ B [0]
   (. 4) B [2] = G [2]
   (. 5) B [ . 1] = B [2] ^ G [. 1]
   (. 6) B [0] = B [. 1] ^ G [0]
   

ASCII code: American Standard Code for Information Interchange

Parity codes (codes having error detection capability): adding a code bit so that a code group number contained odd (odd parity) or even (even parity) on the basis of the original code group

4. The basic logic operations

And logic: only determine all the conditions of an event are in place, it was established; there are one or more conditions are not met, then the event is not established (denoted by F = AB)

Or logic: In the event of a decision to a variety of conditions, as long as there is one or more conditions are met, the establishment of this matter; only when all the conditions are not met, it just does not hold (F = A + B. )

Logical NOT: Assume events F set up or not have it or not related with condition A, if A has, then F is not established; if A is not available, then the establishment of F (F = non-A).

The composite logic operation

Logical NAND: logic and non-logical combination (F = non (AB))

Logical NOR: logical and non-logical OR combination (F = non (A + B))

Logic and non-: a combination of three logical NOR made (F = Non (AB + CD))

Logical XOR (F = AB + A non-non B = A⊕B)

A logical NOR (F = non-A non-B + AB = A⊙B)

6. The logic and negative logic level

Positive logic: high V [H] represents a logical 1, the low level V [L] represents a logical 0

Negative: positive logic opposite

V [H] and the value of V [L] may be a non-overlapping range, by a variety of specific values ​​used in the integrated circuit and the power supply voltage may be applied

7. The basic rules and rules of logic algebra

Logic function is equal to: with two logic function F [1] = f [1] (A [1], A [2], ..., A [n]), F [2] = f [2] (A [1], a [2], ..., a [n]). If for a [1], a [2], ..., a [n] is any set of values, F [1] and F [2 ] are equal, called F [1] and F [2] is equal (if the truth table of the same two logical functions, two functions must be equal)

Basic law

Three rules

1. Is substituted into the rule: any equation containing a variable x, if x is all occurrences are replaced with a logical function formula F, then the equation still holds
2. Inversion rule: Let F be any logical expression, F if all operators, constants and variables converted as follows:
   the resulting new logical formula F is the inverse function, referred to as non F
   (. 1) functions to maintain the original the order of operations between the variable
   (2) is not part of the original formula unchanged the number of non univariate
3. Dual rule: Let F be any logical expression, if all the operators F, conversion constants as follows:
   
   the resulting new logical formula F is the dual type, referred to as F '
   (. 1) held between the primitive variables the order of operations
   (2) is not the original function of the variable transformation
   (3) the dual univariate own formula
   (4) if two logical expressions F and G are equal, are equal to the respective dual formula F 'and G'

Common formula:

1. Elimination Law: AB + A non-B = A
2. Absorption rate: A + AB = A (left short length containing short)
3. Absorption rate: A + Non AB = A + B (containing anti-removed long-trans)
4. Rate comprising: AB + non AC + BC = AB + non-AC (positive or negative relative to the whole remainder End)