ALTERNATIVE LOGIC CIRCUIT

These are gates that are formed from combination of two logic gates. There are two types of alternative logic gate:

NAND GATE

A NAND gate is the combination of an AND gate and NOT gate. It operates the same as an AND gate but the output will be opposite. Remember, the NOT gate does not always have to be the output leg; it could be used to invert an input signal also.

LOGIC SYMBOL FOR THE “NAND” GATE

Notice the circle on output C.

TRUTH TABLE FOR THE “NAND” GATE

INPUT	INPUT	OUTPUT
A	B	C
0	0	1
0	1	1
1	0	1
1	1	0

NAND GATE EQUATION

The NAND gate operation can also be expressed by a Boolean algebra equation. For a 2 – input NAND gate, the equation is:

X = A.B

This equation read X equal to A and B NOT, which simply means that the output of the gate is not a logic 1 when A and B inputs are their 1 states.

NOR GATE

A NOR gate is the combination of both an OR gate and NOT gate. It operates the same as an OR gate, but the output will be the opposite.

TRUTH TABLE FOR THE “NOR” GATE

INPUT	INPUT	OUTPUT
A	B	C
0	0	1
0	1	0
1	0	0
1	1	0

NOR GATE EQUATION

The NOR gate operation can also be expressed by a Boolean algebra equation. For a 2 – input NAND gate, the equation is:

X = A + B

The expression is the same as the OR gate with an over bar above the entire portion of the equation representing the input. This equation read X equal to A or B NOT, which simply means that the output of the gate is not a logic 1 when A or B are in their 1 states.

USES OF LOGIC GATES

Logic gates are in fact the building block of digital electronics, they are formed by the combination of transistors (either BJT or MOSFET) to realise some digital operations like logical OR, NOT, AND etc. Every digital product like computers, mobile phones, calculators, even digital watches contains logical gates.

XOR GATE

The XOR (exclusive – OR) gate acts in the same way as the logical “either or”. The output is “True” if either but not both, of the inputs are “true”. The output is “false” or if both inputs are “true”.

LOGIC SYMBOL FOR “XOR” GATE

TRUTH TABLE FOR THE “XOR” GATE

INPUT	INPUT	OUTPUT
A	B	Y
0	0	0
0	1	1
1	0	1
1	1	0

XOR COMPARATOR

Comparator is a combinational logic circuit that compares the magnitudes of two binary quantities to determine which one has the greater magnitude. In order word, comparator determines the relationship of two binary quantities. A XOR can be used as basic comparator.

As you can see, the only difference between these two symbols is that the XNOR has a circle on its output to indicate that the output is inverted.

One of the most common uses for XOR gates is to add two binary numbers. For this operation to work, the XOR gate must be used in combination with an AND gate.

To understand how the circuit works, review how binary addition works:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10

If you wanted, you could write the results of

each of the preceding addition statements by

using two binary digits, like this:

0 + 0 = 00

0 + 1 = 01

1 + 0 = 01

1 + 1 = 10

When results are written with two binary digits, as in this example, you can easily see how to use an XOR and an AND circuit in combination to perform binary addition.

If you consider just the first binary digit of each result, you’ll notice that it looks just like the truth table for an AND circuit and that the second digit of each result looks just like the truth table for an XOR gate.

The adder circuit has two outputs. The first is called the Sum, and the second is called the Carry. The Carry output is important when several adders are used together to add binary numbers that are longer than 1 bit.