Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function...
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Transcript of Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function...
![Page 1: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/1.jpg)
Digital Electronics
Universal Gate – NAND
![Page 2: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/2.jpg)
Universal Gate – NANDThis presentation will demonstrate• The basic function of the NAND gate.
• How a NAND gate can be used to replace an AND gate, an OR gate, or an INVERTER gate.
• How a logic circuit implemented with AOI logic gates can be re-implemented using only NAND gates.
• That using a single gate type, in this case NAND, will reduce the number of integrated circuits (IC) required to implement a logic circuit.
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AOI Logic NAND Logic
More ICs = More $$ Less ICs = Less $$
![Page 3: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/3.jpg)
NAND Gate
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X Y Z
0 0 1
0 1 1
1 0 1
1 1 0
X
YY X YXZ
![Page 4: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/4.jpg)
NAND Gate as an Inverter Gate
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X Z
0 1
1 0
X XZ
XXX (Before Bubble)
Equivalent to Inverter
![Page 5: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/5.jpg)
NAND Gate as an AND Gate
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X Y Z
0 0 0
0 1 0
1 0 0
1 1 1
X
Y YX YXZ
YX
NAND Gate Inverter
Equivalent to AND Gate
![Page 6: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/6.jpg)
NAND Gate as an OR Gate
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X Y Z
0 0 0
0 1 1
1 0 1
1 1 1
Equivalent to OR Gate
X
Y
YXY X Y XZ
X
NAND GateInverters
Y
![Page 7: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/7.jpg)
NAND Gate Equivalent to AOI Gates
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INVERTERORAND
![Page 8: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/8.jpg)
Process for NAND Implementation1. If starting from a logic expression, implement the design
with AOI logic.
2. In the AOI implementation, identify and replace every AND,OR, and INVERTER gate with its NAND equivalent.
3. Redraw the circuit.
4. Identify and eliminate any double inversions (i.e., back-to-back inverters).
5. Redraw the final circuit.
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![Page 9: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/9.jpg)
NAND Implementation
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Example:
Design a NAND Logic Circuit that is equivalent to the AOI circuit shown below.
CA C B
![Page 10: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/10.jpg)
NAND Implementation
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Solution – Step 2
Identify and replace every AND,OR, and INVERTER gate with its NAND equivalent.
![Page 11: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/11.jpg)
NAND Implementation
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Redraw the circuit.
Solution – Step 3
![Page 12: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/12.jpg)
NAND Implementation
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Identify and eliminate any double inversions.
Solution – Step 4
![Page 13: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/13.jpg)
NAND Implementation
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Solution – Step 5
Redraw the circuit.
![Page 14: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/14.jpg)
Proof of Equivalence
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C C B
C AC A C BZ
C AC BZ
CA C B
![Page 15: Digital Electronics Universal Gate – NAND. This presentation will demonstrate The basic function of the NAND gate. How a NAND gate can be used to replace.](https://reader036.fdocuments.in/reader036/viewer/2022081516/56649f095503460f94c1d9db/html5/thumbnails/15.jpg)
AOI vs. NAND
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IC Type Gates Gate / IC # ICs
74LS04 1 6 1
74LS08 2 4 1
74LS32 1 4 1
Total Number of ICs → 3
IC Type Gates Gate / IC # ICs
74LS00 4 4 1
Total Number of ICs → 1