Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
This helps in Digital Logic Design
Typology: Cheat Sheet
1 / 12
This page cannot be seen from the preview
Don't miss anything!
Name Reg. No. Marks
The objectives of this experiment are:
A universal gate is a gate that can implement any Boolean function without needing to use any other gate type. The NAND and NOR gates are universal gates. In practice, this is advantageous since NAND and NOR gates are economical and easier to fabricate and are the basic gates used in all IC digital logic families. An AND gate is typically implemented as a NAND gate followed by an inverter, not vice versa. Likewise, an OR gate is typically implemented as a NOR gate followed by an inverter, not vice versa.
The NAND (Not – AND) gate has an output that is normally at logic level “1” and only goes “LOW” to logic level “0” when ALL its inputs are at logic level “1”. The Logic NAND Gate is the reverse or “Complementary” form of the AND gate we have seen previously. The logic or Boolean expression given for a logic NAND gate is that for Logical Addition, which is the opposite to the AND gate, and which it performs on the complements of the inputs. The Boolean expression for a logic NAND gate is denoted by a single dot or full stop symbol, (.) with a line or Overline, ( ‾‾ ) over the expression to signify the NOT or logical negation of the NAND gate giving us the Boolean expression of: A.B = Q. Then we can define the operation of a 2-input digital logic NAND gate as being: “If both A and B are true, then Q is NOT true.” Logic NAND Gates are available using digital circuits to produce the desired logical function and are given a symbol whose shape is that of a standard AND gate with a circle, sometimes called an “inversion bubble” at its output to represent the NOT gate symbol with the logical operation of the NAND gate as shown in Figure 4.2. Figure 4.2 Symbol of 2-input NAND gate Figure 4.1 NAND gate implementation using AND and NOT gates.
Figure 4.5 NOR gate equivalent The logic or Boolean expression given for a logic NOR gate is that for Logical Multiplication which it performs on the complements of the inputs. The Boolean expression for a logic NOR gate is denoted by a plus sign, (+) with a line or Overline, (‾‾) over the expression to signify the NOT or logical negation of the NOR gate giving us the Boolean expression of: A+B = Q. Then we can define the operation of a 2-input digital logic NOR gate as being: “If both A and B are NOT true, then Q is true.” Logic NOR Gates are available using digital circuits to produce the desired logical function and are given a symbol whose shape is that of a standard OR gate with a circle, sometimes called an “Inversion bubble” at its output to represent the NOT gate symbol with the logical operation of the NOR gate as shown in Figure 4.6. Figure 4.6 Symbol of 2-input NOR gate As with the OR function, the NOR function can also have any number of individual inputs, and commercially available NOR Gate ICs are available in standard 2, 3, or 4 input types. If additional inputs are required, then the standard NOR gates can be cascaded together to provide more inputs for example. Figure 4.7 4-input NOR function The Boolean Expression for this 4-input NOR gate will therefore be: Q = A+B+C+D If the number of inputs required is an odd number of inputs any “unused” inputs can be held LOW by connecting them directly to ground using suitable “Pull-down” resistors. The Logic NOR Gate function is sometimes known as the Pierce Function and is denoted by a downwards arrow operator as shown, A↓B.
Like the NAND gate seen in the last section, the NOR gate can also be classed as a “Universal” type gate. NOR gates can be used to produce any other type of logic gate function just like the NAND gate and by connecting them in various combinations the three basic gate types of AND, OR, and NOT function can be formed using only NOR gates, for example. Figure 4.8 Logic gates using only NOR gates. As well as the three common types above, Exclusive-OR, Exclusive-NOR, and standard NOR gates can also be formed using just individual NOR gates.
Table 4.1 Observation table of 1st^ IC
Pin Number Logic / State Pin Number Logic / State Pin Number Logic / State 1 0 2 0 3 1 1 0 2 1 3 1 1 1 2 0 3 1 1 1 2 1 3 0
Pin Number Logic / State Pin Number Logic / State Pin Number Logic / State 2 0 3 0 1 1 2 0 3 1 1 0 2 1 3 0 1 0 2 1 3 1 1 0 Table 4.3 Observation table of 4 inputs-based NAND gate implementation
0 0 0 1 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 1 0 1 1 0 1 0 1 1 1 1 0 0 0 0 1 1 0 1 1 1 1 0 0 0 1 1 0 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 0 0 0 Table 4.4 Observation table of 4 inputs based NOR gate implementation.
0 0 0 1 0 0 0 1 0 0 0 0 1 1 0 0 1 0 0 0
Table 2.7 Result Summary Sr No IC Number Type of Gate 1 7400 NAND Gate 2 7402 NOR Gate
The two necessary connections are:
Yes. If both inputs of a NOR gate are connected to the same input , it behaves as a NOT gate. Example: Input = A Output = (𝐴+𝐴)′^ =𝐴′ So NOR can also work as an inverter.
Assessment Rubrics CSE-105L – Digital Logic Design
Method: Lab reports, viva, and instructor observation during lab sessions. Outcome Assessed:
