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barcode reader code in asp.net c# B OR C in Software
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A B A B
(A + B) = A B
(A B) (A + B) A 0 0 1 1 B 0 1 0 1 A 1 1 0 0 NAND gate
B 1 0 1 0 (A B) 1 1 1 0 A 0 0 1 1 B 0 1 0 1 A 1 1 0 0 NOR gate
B 1 0 1 0 (A + B) 1 0 0 0 Figure 1321 Equivalence of NAND and NOR gates with AND and OR gates
In the next section we shall learn how to systematically approach the design of logic functions First, we provide a few examples to illustrate logic design with NAND and NOR gates EXAMPLE 136 Realizing the AND Function with NAND Gates
Problem
Use a truth table to show that the AND function can be realized using only NAND gates, and show the physical realization Solution
Known Quantities: AND and NAND truth tables
13
Digital Logic Circuits
A 0 1 A
B(= A) 0 1 AB 0 1
(AB) 1 0 Find: AND realization using NAND gates Assumptions: Consider twoinput functions and gates Analysis: The truth table below summarizes the two functions: NAND
A NOT A
B 0 1 0 1 NAND A B 1 1 1 0
AND A B 0 0 0 1
Figure 1322 NAND gate as an inverters
A B AB
0 0 1 1 NAND
NAND
Clearly, to realize the AND function we need to simply invert the output of a NAND gate This is easily accomplished if we observe that a NAND gate with its inputs tied together acts as an inverter; you can verify this in the above truth table by looking at the NAND output for the input combinations 00 and 11, or by referring to Figure 1322 The nal realization is shown in Figure 1323 Comments: NAND gates naturally implement functions that contain complemented
products Gates that employ negative logic are a natural consequence of the inverting characteristics of transistor switches (refer to Section 105) Thus, one should expect that NAND (and NOR) gates are very commonly employed in practice EXAMPLE 137 Realizing the AND Function with NOR Gates
Problem
Show analytically that the AND function can be realized using only NOR gates, and determine the physical realization A 0 1 B( = A) (A + B) (A + B) 0 0 1 1 1 0 Solution
Known Quantities: AND and NOR functions Find: AND realization using NOR gates Assumptions: Consider twoinput functions and gates Figure 1324 NOR gate as an inverter
A NOR B NOR B (A + B) = AB
Analysis: We can solve this problem using De Morgan s theorem The output of an AND gate can be expressed as f = A B Using De Morgan s theorem we write: f =f =A B =A+B The above function is implemented very easily if we see that a NOR gate with its input tied together acts as a NOT gate (see Figure 1324) Thus, the logic circuit of Figure 1325 provides the desired answer Comments: NOR gates naturally implement functions that contain complemented sums
Gates that employ negative logic are a natural consequence of the inverting characteristics of transistor switches (refer to Section 105) Thus, one should expect that NOR (and NAND) gates are very commonly employed in practice Part II
Electronics
EXAMPLE 138 Realizing a Function with NAND and NOR Gates
Problem
Realize the following function using only NAND and NOR gates: y = (A B) + C
A B C
Solution
Known Quantities: Logical expression for y Find: Realization of y using only NAND and NOR gates Assumptions: Consider twoinput functions and gates Analysis: On the basis of the two preceding examples, we see that we can realize the

