Programming --> Logic

Programming Logic One and Two Input Gates Three Input Gates Boolean Algebra Theorems Useful Logical Programming Tools Notes Other Resources One and Two Input Gates AND Gate NAND Gate Output is TRUE only if both inputs are TRUE. Output is FALSE only if both inputs are TRUE. A    B output F    F F F    T F T    F F T    T T        A    B output 0    0 0 0    1 0 1    0 0 1    1 1 (The AND gate is useful for masking or clearing specified bit positions.) A    B output F    F T F    T T T    F T T    T F        A    B output 0    0 1 0    1 1 1    0 1 1    1 0 OR Gate NOR Gate Output is TRUE if either input (or both) is TRUE. Output is FALSE if either input (or both) is TRUE. A    B output F    F F F    T T T    F T T    T T        A    B output 0    0 0 0    1 1 1    0 1 1    1 1 (The OR gate is useful for setting specified bits.) A    B output F    F T F    T F T    F F T    T F        A    B output 0    0 1 0    1 0 1    0 0 1    1 0 XOR (EXCLUSIVE OR) Gate XNOR (EXCLUSIVE NOR) Gate (or Equality Gate) Output is TRUE if either input (but not both) is TRUE. Output is FALSE if either input (but not both) is TRUE. A    B output F    F F F    T T T    F T T    T F        A    B output 0    0 0 0    1 1 1    0 1 1    1 0 (The XOR gate is useful for complementing specified bits.) A    B output F    F T F    T F T    F F T    T T        A    B output 0    0 1 0    1 0 1    0 0 1    1 1 NOT Function (or Inverter or Complement Function)     A output F T T F        A output 0 1 1 0 (The NOT function is useful for complementing every bit.)   Three Input Gates AND Gate NAND Gate Output is TRUE only if all inputs are TRUE. Output is FALSE only if all inputs are TRUE. A    B    C output F    F    F F F    F    T F F    T    F F F    T    T F T    F    F F T    F    T F T    T    F F T    T    T T        A    B    C output 0    0    0 0 0    0    1 0 0    1    0 0 0    1    1 0 1    0    0 0 1    0    1 0 1    1    0 0 1    1    1 1 A    B    C output F    F    F T F    F    T T F    T    F T F    T    T T T    F    F T T    F    T T T    T    F T T    T    T F        A    B    C output 0    0    0 1 0    0    1 1 0    1    0 1 0    1    1 1 1    0    0 1 1    0    1 1 1    1    0 1 1    1    1 0 OR Gate NOR Gate Output is TRUE if any input (or all) is TRUE. Output is FALSE if any input (or all) is TRUE. A    B    C output F    F    F F F    F    T T F    T    F T F    T    T T T    F    F T T    F    T T T    T    F T T    T    T T        A    B    C output 0    0    0 0 0    0    1 1 0    1    0 1 0    1    1 1 1    0    0 1 1    0    1 1 1    1    0 1 1    1    1 1 A    B    C output F    F    F T F    F    T F F    T    F F F    T    T F T    F    F F T    F    T F T    T    F F T    T    T F        A    B    C output 0    0    0 1 0    0    1 0 0    1    0 0 0    1    1 0 1    0    0 0 1    0    1 0 1    1    0 0 1    1    1 0 XOR (EXCLUSIVE OR) Gate XNOR (EXCLUSIVE NOR) Gate A    B    C output F    F    F F F    F    T T F    T    F T F    T    T F T    F    F T T    F    T F T    T    F F T    T    T T        A    B    C output 0    0    0 0 0    0    1 1 0    1    0 1 0    1    1 0 1    0    0 1 1    0    1 0 1    1    0 0 1    1    1 1 A    B    C output F    F    F T F    F    T F F    T    F F F    T    T T T    F    F F T    F    T T T    T    F T T    T    T F        A    B    C output 0    0    0 1 0    0    1 0 0    1    0 0 0    1    1 1 1    0    0 0 1    0    1 1 1    1    0 1 1    1    1 0 Boolean Algebra Theorems AND theorems 0 · 0 = 0 A · 1 = A 1 · 1 = 1 A · A = A 1 · 0 = 0 A · /A = 0 A · 0 = 0   OR theorems 1 + 1 = 1 A + 0 = A 0 + 0 = 0 A + A = A 1 + 0 = 1 A + /A = 1 A + 1 = 1   NOT /0 = 1 /1 = 0 //A = A   Commutation A + B = B + A A · B = B · A Absorption A + A · B = A A · (A + B) = A Association A + (B + C) = (A + B) + C A · (B · C) = (A · B) · C Distribution A + B · C = (A + B) · (A + C) A · (B + C) = A · B + A · C DeMorgan's theorems /A + /B = /A · /B /A · /B = /A + /B Useful Logical Programming Tools IF N AND 1 THEN Tests if a number is odd (has its bit 1 set) N + N AND -2 Always gives the even number of a pair, so if you are calculating an offset into a buffer, this always places you at an even-numbered position. N = N AND X Keeps a variable within a range X. So N AND 16383 insures that an integer never exceeds 16383. N = N AND 127 Clears the high bit (bit 8) in characters such as for sending to a serial port. N = N OR 128 Sets the high bit (bit 8) in characters. In some cases this signals an attribute such as underlining. N = N AND 95 Changes an lower case ASCII letter character to upper case by clearing bit 6. Replaces IF (ASCII CODE N) > 96 THEN N = N - 32. N = N OR 32 Changes an upper case ASCII letter character to lower case by setting bit 6. N = N AND 15 Converts an ASCII number character into its decimal number value by clearing bits 5 and 6. N = N OR 48 Converts the digits 0 to 9 into their printable ASCII codes by setting bits 5 and 6. IF X OR Y If either X or Y has a nonzero value ... X = X XOR 1 Sets a flag variable from 1 or -1 to 0 and back. Replaces IF X THEN X = 0 ELSE X = 1. PAGE = PAGE XOR 3 XOR can be used jump back and forth between two values, here between video pages 1 and 2. The value that toggles between has 1's where changes occur and 0 where they don't, for example to switch between   3  00000011 and 45  00101101 use 46  00101110 X = X + 1 AND 3 This can be used to maintain a cycle. Replaces X = X + 1: IF X = 4 THEN X = 0. X = 1 - X Toggles a variable between 1 and 0. Notes FALSE = F = 0 TRUE = T = 1   Positive Logic (or Positive True Logic or High True Logic) FALSE or 0 = LOW TRUE or 1 = HIGH   Negative Logic (or Negative True Logic or Low True Logic) FALSE or 0 = HIGH TRUE or 1 = LOW   Bit_Logic.vi:  A LabVIEW program that demonstrates bit-wise logic operations. Other Resources Binary Arithmetic Digital Logic Gates [  Index  |  Technical Notes  ] DISCLAIMER Page author: Dawn Rorvik (rorvikd@evergreen.edu) Last modified: 11/17/2006