Converting AND-OR expression to NAND-NAND?

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In summary, the conversation is about creating a BCD 3321 encoder using DeMorgan's Law and NAND-NAND logic. The speaker has already completed a truth table and derived logical expressions for each bit, but is having trouble converting their AND-OR logic expressions into NAND-NAND logic. The other person suggests double negating the equations and applying DeMorgan's Law to achieve the desired logic.
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Noopi
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Homework Statement


Make a BCD 3321 encoder. So if you input 0100, the encoder will output (depending on your design) either a 1001, or a 0101. Similarly, an input of 0101 will output either a 1010 or a 0110 (again, depending on your design).

Homework Equations


I know you're supposed to use DeMorgan's Law, but I have a hard time understanding WHEN to use it.

The Attempt at a Solution


I have done the truth table, the kmaps, and derived the logical expressions for each bit, but what I'm having a hard time doing is turning my AND-OR logic expressions into NAND-NAND logic expressions.

My 4 logical expressions are:

(3) MSB: A + BC
(3) Second MSB: A + B + CD
(2) Third MSB: A + BC'D + B'CD'
(1) LSB: BCD + BC'D' + B'C'D

My professor mentioned something about double negating the equations, and then applying DeMorgan's Law to get the NAND-NAND logic, and that's where he lost me.

Any help will be greatly appreciated!
 
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Keep in mind that in the logic diagram

you will implement it in two-level NAND gate

for example if you have this function f(w,x,y )=xy+xz+w

In the first level you will have (xy)' , (xz)' , w'

Then the second level [(xy)'(xz)'w']'=xy+xz+w
 

What is the purpose of converting an AND-OR expression to NAND-NAND?

The purpose of converting an AND-OR expression to NAND-NAND is to simplify the expression and make it easier to implement in digital logic circuits. NAND gates are the universal gates, meaning that any logical expression can be represented using only NAND gates. This simplification can help reduce costs and improve efficiency in circuit design.

How do you convert an AND-OR expression to NAND-NAND?

To convert an AND-OR expression to NAND-NAND, you can use De Morgan's laws and the fact that NAND gates are the negation of AND gates. First, you need to apply De Morgan's laws to change the AND and OR operators to NAND operators. Then, you can use the property that NAND gates can be used to negate inputs to create a series of NAND gates that represent the original AND-OR expression.

What are the advantages of using NAND-NAND logic over AND-OR logic?

One of the main advantages of using NAND-NAND logic is that it allows for simpler and more compact circuit design. Since NAND gates are universal gates, they can be used to represent any logical expression, making it easier to implement complex logic circuits. Additionally, using only NAND gates can help reduce costs and improve efficiency in circuit design.

Are there any disadvantages to converting to NAND-NAND logic?

One potential disadvantage of converting to NAND-NAND logic is that the resulting circuit may be more difficult to understand and troubleshoot, since it may not be as intuitive as using AND-OR logic. Additionally, converting to NAND-NAND logic may not always result in a more efficient circuit, as it depends on the specific expression and circuit design.

What other types of logic gates can be used to simplify expressions?

In addition to NAND gates, NOR gates are also universal gates, meaning they can be used to represent any logical expression. Other types of logic gates, such as XNOR gates, can also be used to simplify expressions. However, NAND and NOR gates are the most commonly used due to their versatility and efficiency in circuit design.

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