Question

Draw the AND OR circuit for:


y=( refer the picture for the other part of the equation)​

Answer 1

Answer:

Explanation:

the input and output information of any Logic Gate or circuit can be plotted into a standard table to give a visual representation of the switching function of the system.

The table used to represent the boolean expression of a logic gate function is commonly called a Truth Table. A logic gate truth table shows each possible input combination to the gate or circuit with the resultant output depending upon the combination of these input(s).

For example, consider a single 2-input logic circuit with input variables labelled as A and B. There are “four” possible input combinations or 22 of “OFF” and “ON” for the two inputs. However, when dealing with Boolean expressions and especially logic gate truth tables, we do not general use “ON” or “OFF” but instead give them bit values which represent a logic level “1” or a logic level “0” respectively.

Then the four possible combinations of A and B for a 2-input logic gate is given as:

Input Combination 1. – “OFF” – “OFF” or ( 0, 0 )

Input Combination 2. – “OFF” – “ON” or ( 0, 1 )

Input Combination 3. – “ON” – “OFF” or ( 1, 0 )

Input Combination 4. – “ON” – “ON” or ( 1, 1 )

Therefore, a 3-input logic circuit would have 8 possible input combinations or 23 and a 4-input logic circuit would have 16 or 24, and so on as the number of inputs increases. Then a logic circuit with “n” number of inputs would have 2n possible input combinations of both “OFF” and “ON”.

So in order to keep things simple to understand, in this tutorial we will only deal with standard 2-input type logic gates, but the principals are still the same for gates with more than two inputs.

Then the Truth tables for a 2-input AND Gate, a 2-input OR Gate and a single input NOT Gate are given as:

2-input AND Gate

For a 2-input AND gate, the output Q is true if BOTH input A “AND” input B are both true, giving the Boolean Expression of: ( Q = A and B ).

Symbol Truth Table

boolean algebra AND gate truth table A B Q

0 0 0

0 1 0

1 0 0

1 1 1

Boolean Expression Q = A.B Read as A AND B gives Q

Note that the Boolean Expression for a two input AND gate can be written as: A.B or just simply AB without the decimal point.

2-input OR (Inclusive OR) Gate

For a 2-input OR gate, the output Q is true if EITHER input A “OR” input B is true, giving the Boolean Expression of: ( Q = A or B ).

Symbol Truth Table

boolean algebra OR gate truth table A B Q

0 0 0

0 1 1

1 0 1

1 1 1

Boolean Expression Q = A+B Read as A OR B gives Q

NOT Gate (Inverter)

For a single input NOT gate, the output Q is ONLY true when the input is “NOT” true, the output is the inverse or complement of the input giving the Boolean Expression of: ( Q = NOT A ).

Symbol Truth Table

boolean algebra NOT gate truth table A Q

0 1

1 0

Boolean Expression Q = NOT A or A Read as inversion of A gives Q

The NAND and the NOR Gates are a combination of the AND and OR Gates respectively with that of a NOT Gate (inverter).

2-input NAND (Not AND) Gate

For a 2-input NAND gate, the output Q is NOT true if BOTH input A and input B are true, giving the Boolean Expression of: ( Q = not(A AND B) ).