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

NAND and NOR gates are called Universal gates, because the fundamental logic gates can be realized through them

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 O.

a) AND gate truth table

A	B	C
0	0	0
0	1	0
1	0	0
1	1	1

b) OR Gate Truth table

A	B	C
0	0	0
0	1	1
1	0	1
1	1	1

c) Not Gate Truth Table

A	A
0	1
1	0

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

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 Systenm - Radix 8
Decimal Number System - Radix 10
Hexadecimal Number System - Radix 16.

AND and OR operation from NAND gates are shown below

A.B = (A NAND B) NAND ( A NAND B)
OR operation

A+B (ANAND A)NAND (B NANDY Y)
b) AND AND OR operation from NOR gates are shown below.

A - B = (A NORA A) NOR (B NOR B)

A+ B = (A NOR B) NOR (A NOR B)

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 0. 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 'I'. 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 ifboth inputs are 0,
C = A.B
= 0 .0 
= 0
The Truth Table For AND Gate is

Input		Output
A	B	C
0	0	0
0	1	0
1	0	0
1	1	1

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

Input		Output
A	B	C
0	0	0
0	1	1
1	0	0
1	1	1

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

Input	Output
A	C
1	0
0	1

a. 1101010₂ + 101101₂
1101010
+101101
________
10010111
________
1101010₂ + 101101₂ = 10010111₂
b. 1101011₂ - 111010₂
1101011
+111010
_______
0110001
_______
1101011₂ - 111010₂ = 110001₂