Short the inputs together.
Logic: A High input, with the inputs shorted together, will be H+H at the input side of the NAND gate, therefore resulting in a low output.
A Low input, with both inputs shorted together, is L+L for inputs, resulting in a High output.
Also, a NOR gate can be used in exactly the same way.
A: NAND implies not and to be true both input must be hi or true <> There are two flavors of NAND gate. The positive input/negative output NAND will have a low output if and only if both inputs are high. The negative input/positive output NAND will have a high output if and only if both inputs are low.
To make a full subtractor, you need an XOR and a NAND gate.
Next: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates ContentsUsing NAND gatesNOTFigure 12.10: Realizing a NOT gate using a NAND gateOR The following statements are called DeMorgan's Theorems and can be easily verified and extended for more than two variables.(12.1)(12.2)(12.3)(12.4)In general: (12.5)Thus :(12.6)Now it is easy to see that , which can be checked from the truth table easily. The resulting realization of OR gate is shown in 12.11Figure 12.11: Realization of OR gate by NAND gatesAND gateFigure 12.12: Realization of AND gate by NAND gatesX-OR gate(12.7)Clearly, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates.Figure 12.13: X-OR gateX-NOR gate(12.8)Again, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates, i.e., NAND or NOR gates.Figure 12.14: X-NOR gateNext: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates Contentsynsingh 2007-07-25
by the procedure design a half subtractor design a logic ciruit to add two numbers with five bits each drawthe logic diagram of afull adder using using NAND gates only ?
because it is an universal gate that control and repairs other gates.
when the two inputs are shorted, a NAND gate acts like a NOT gate. hence AND = NAND + NOT For OR gate, inverse both the inputs before connecting them to a NAND gate. So three NAND gates would be needed.
When the two input terminals of a NAND gate are short circuited, it acts as a NOT gate.
NOT Gate
Connect the two inputs of the NAND gate together.
pass the inputs through an nand gate and again pass them through inverter,which is again formed by an nand gate
yes (a or b)' = a' and b' a or b = (a' and b')' a or b = a' nand b'
You can construct a NAND gate using relays. If the contacts are in series, it is an AND gate. If the contacts are in parallel, it is an OR gate. Depending on which contact you use, it is a NOT gate. Simply pick the right combination of contacts and the meaning of the signal, and you can consider it to be a NAND gate.
XORing X with 1 gives X', i.e., NOT(X). If we are able to construct a NAND (AND) using XOR, we can also obtain AND (NAND) from it, which makes XOR a universal gate since inverted inputs to a NAND (AND) will give OR (NOR). However XOR is not a universal gate! Therefore we cannot obtain NAND (AND) using XOR. :-) By, Tirtha Sarathi Ghosh Class 10 IIT Kanpur Aspirant
NAND gate
A&B = ((A&B)')' So two, it would go a - | ==NAND--=NAND-- b - | By using two NAND gates back-to-back, you can create a normal AND gate.
the not gate applied to and gate is nand gate
Next: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates ContentsUsing NAND gatesNOTFigure 12.10: Realizing a NOT gate using a NAND gateOR The following statements are called DeMorgan's Theorems and can be easily verified and extended for more than two variables.(12.1)(12.2)(12.3)(12.4)In general: (12.5)Thus :(12.6)Now it is easy to see that , which can be checked from the truth table easily. The resulting realization of OR gate is shown in 12.11Figure 12.11: Realization of OR gate by NAND gatesAND gateFigure 12.12: Realization of AND gate by NAND gatesX-OR gate(12.7)Clearly, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates.Figure 12.13: X-OR gateX-NOR gate(12.8)Again, this can be implemented using AND, NOT and OR gates, and hence can be implemented using universal gates, i.e., NAND or NOR gates.Figure 12.14: X-NOR gateNext: Boolean Expressions Up: Universality of certain gates Previous: Universality of certain gates Contentsynsingh 2007-07-25