# Which is the logical equation in physics

## Physics compact 7, special issue

Digital electronics 4.2 RG 6.4 and G 6.4 23 A1 Use the function table to check that the above circuit actually works like an AND gate! The NOR gate: Investigate the behavior of a NOR gate with the TTL-IC 7402 (4 NOR gates): E2 A4 Set up the specified circuit and check with a complete function table whether it looks like an OR gate behaves! AB A '= (A ^ A)' B '= (B ^ B)' (A '^ B') '0 0 0 1 1 0 1 1 We summarize: Every logic circuit can be implemented with the help of NAND gates become. When experimenting, the LEDs for displaying the logical status of a TTL output can be connected directly to ground via an ohmic resistance of 100-470 X. If several displays are required, it is better to amplify the output signals via transistors: The output signal of the TTL IC is connected to the base of the transistor via a 3.3 k X resistor, the LED is in the emitter circuit, the equivalent gate (the equivalent gate) An equivalence gate checks whether two inputs have the same logical value. We consider: The same logical value is present at the two inputs if a) both inputs E 1 and E 2 are equal to 1 or b) both inputs E 1 and E 2 are equal to 0. Since output A should be a logical " 1 ”if they are equal, we test the input value“ 0 ”with the aid of an inverter and in this case get a logical“ 1 ”. Finally, we combine two AND gates with an OR gate (Fig. 24.2). E1 AB & & & Z Fig. 23.2 + - 470 3.3 k E BC 547 Fig. 23.3 14 1 13 2 12 3 11 4 10 5 9 6 8 7 US> 1> 1> 1> 1 Fig. 23.1 A2 Show in the experiment the validity of the law of double negation (A ')' = A! The Laws of De Morgan (De Morgan's Laws) With digital circuits we process the logical values "0" and "1". Variables for logical values fulfill the following two equations: (A v B) '= A' ^ B '(Laws of De Morgan) (A ^ B)' = A 'v B' With a table showing all possible truth values For the taking inputs A and B into account, laws like De Morgan's laws can be proven. We calculate that (A v B) '= A' ^ B ': ABA v B (A v B)' A 'B' A '^ B' 0 0 0 1 1 1 1 0 1 1 0 1 0 0 1 0 1 0 0 1 0 1 1 1 0 0 0 0 Since for all assignments of the two inputs A and B in the third column (left side of De Morgan's law) and in the fifth column (right side of De Morgan) the same value occurs, the validity of De Morgan's law has been proven. By applying the mathematical laws, expressions with truth values can be transformed. For example, the following applies to the OR link: A v B = ((A v B) ')' = (A '^ B') 'Electronically, the OR gate (left side) can be replaced by a few NAND gates (right side) be replaced. A3 Calculate that (A ^ B) '= A' v B 'applies! A B A ^ B (A ^ B) ’A’ B ’A’ v B ’0 0 0 1 1 1 1 0 1 1 0 1 1 E1 W1 For testing purposes only - property of the publisher Öbv

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