The truth table for XOR gate is

The NAND is the combination of NOT and AND. The NAND is generated by inverting the output of an AND operator. The algebraic expression of the NAND function is : Y = A . B

Boolean algebra is a mathematical discipline that is used for designing digital circuits in a digital computer. It describes the relation between inputs and outputs of a digital circuit. The name Boolean algebra has been given in honor of an English mathematician George Boole who proposed the basic principles of this algebra.

46₁₀ - 101110₂

Step 1: Convert given Decimal number into Binary.
Step 2: Check if the binary number contains 8 bits. if less add 0 at the left most bit, to make it as 8 bits.
Step 3: Invert all bits (i.e. Change 1 as 0 and 0 as 1).

The term data comes from the word datum, which means a raw fact. The data is a fact about people. places or some objects

The XNOR (exclusive - NOR) gate is a combination XOR gate followed by an inverter. Its output is "true" if the inputs are the same, and "false" if the inputs are different. In simple words, the output is 1 if the input is the same, other wise the output is 0.

a) AND gate truth table

b) OR Gate Truth table

c) Not Gate Truth Table

8 bit Format of 20₁₀  = 00010100
8 bit format of 25₁₀    = 00011001
20₁₀ + 25₁₀              =    _________
                                   00101101
                                    __________
20₁₀ + 25₁₀ = 00101101₂

150₁₀ = ?

150₁₀ = (10010110)₂

10010110₂ = 226₈

(i) There are only two digits in the Binary system, namely, 0 and 1. The numbers in the binary system are represented to the base 2 and the positional multipliers are the powers of 2.
(ii) The left most bit in the binary number is called as the Most Significant Bit (MSB) and it has the largest positional weight.
(iii) The right most bit is the Least Significant Bit (LSB) and has the smallest positional weight.

A numbering system is a way of representing numbers. Each number system is uniquely identified by its base value or radix. Radix or base is the count of number of digits in each number system. Radix or base is the general idea behind positional numbering system.
Example:
Binary Number System - Radix 2
Octal Number System - Radix 8
Deciaml Number System - Radix 10
Hexadecimal Number System - Radix 16.

AND Gate:
The AND gate can have two or more input signals and produce an output signal.
The output is "true" only when both inputs are "true", otherwise, the output is "false". In other words, the output will be 1 if and only if both inputs are 1;  otherwise the output is O. The output of the AND gate is represented by a variable say C, where A and B are two and if input boolean variables. In boolean algebra, a variable can take either of the values '0' or '1'. The logical symbol of the AND gate is AND gate is

One way to symbolize the action of an AND gate by writing the boolean function.
C = A AND B
In boolean algebra the multiplication sign stand for the AND operation. Therefore, the output of the AND gate is
          C = A.B or
Simply C = A .B
Read this as "C equals A AND B". Since there an two input variables here, the truth table has four entries, because there are four possible inputs: 00 01, 10 and 11
For instance both inputs are 0,
C = A.B
   = 0 .0 
    = 0
The Truth Table For AND Gate is

OR Gate:
The OR gate gets its name from the face that behaves like the logical inclusive "OR"  The output is "true" if either or both of the inputs are "true", both inputs are "false" then the output is "false", other words the output will be 1 if and only if 0, or both inputs are 1; otherwise, the output is 0, the logical symbol of the OR gate is

The OR gate output is
C = A or B
We use the + sign to denote the OR function therefore
C = A + B
Read this C equals A or B
For instance, if both the input are 1
C = A + B = 1 + 1 = 1
The truth table For OR Gate is

NOT Gate;
The NOT gate, called a logical inverter, has only one input. It reverses the logical state. In other words the output C is always the complement of the input. The logical symbol of the NOT gate is

The Boolean function of Not Gate is
C = NOT A
In boolean algebra, the overbar stands for NOT operation. Therefore,
C = \(\bar { A } \)
Read This as "C" equals Not "A" or "C" equals the complement of "A''
If A is 0
C = \(\bar { 1 } \) = 0
On the other hand, if A is 1
C = \(\bar { 1 } \) = 0
The truth table for NOT gate is

The method of repeated multiplication by 2 has to be used to convert such kind of decimal fractions.
The steps involved in the method of repeated multiplication by 2:
Step 1: Multiply the decimal fraction by 2 and note. the integer part. The integer part is either 0 or 1.
Step 2: Discard the integer part of the previous product. Multiply the fractional part of the previous product by 2. Repeat Step 1 until the same fraction repeats or terminates (0).
Step 3: The resulting integer part forms a sequence of 0s and 1s that become the binary equivalent of decimal fraction.
Step 4: The final answer is to be written from first. integer part obtained till the last integer part obtained.