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Number System and Conversion Boolean Logic

Perform the Binary Operations as indicated.1. 11111 + 100012. 111001 - 100103. 1111 x 10104. 111101/101

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Define:1. Number system2. Decimal Number system3. Binary Number System4. Octal Number system5. Hexadecimal Number System6. Compliments7. Logic Function8. Boolean Algebra9. Truth table10. Boolean Ex...

Answers:

1. Number System- It refers to the digits, its arrangements, positional weight and the base of the number system.

2. Decimal Number system- A number system having base or radix 10 is known as decimal number system.

3. Binary Number System- A number system having base or radix 2 is known as binary number system.

4. Octal Number system- A number system having base or radix 8 is known as octal number system.

5. Hexadecimal Number System- A number system having base or radix 16 is known as...

2’s compliment

2’s compliment of any binary number is obtained by adding binary ‘1’ to the 1’s compliment of the number.Binary subtraction using 2’s complement:1. Make both the numbers having same number of digit...

1's Compliment

Click here for a general overview of Number System.1’s complement of a binary number is obtained by subtracting each bit by 1. We can get 1’s complement by simply replacing 1 by 0 and 0 by 1. For e...

De Morgan's Law

# First TheoremIt states that “The complement of a sum equals to the product of the complements.”i.e., ➡ (A + B)’ = A’.B’# Second TheoremIt states that “The complement of a product is equal to th...

Distributive Law

It states that the multiplication of two variables and adding the result with a variable will result in the same value as multiplication of addition of the variable with individual variables. Likew...

Associative Law

It allows for the removal of brackets from an expression and regrouping of the variables.i.e. ➡ (A + B) + C = A + (B + C)➡ (A.B).C = A.(B.C) Proof:Hence, (A + B) + C = A + (B + C) & (A.B).C = A...

Commutative Law

It states that the interchanging the order of operands in a Boolean equation doesn’t change its result.i.e., ➡ (A + B) = (B + A) ➡ A.B = B.AProof:Hence, (A + B) = (B + A) & A.B = B.A

Complement Law

It states that when the sum is performed between a variable and its complement, the result is 1. Likewise, when a multiplication is performed between a variable and its complement, the result is ze...

Identity Law

It states that the sum of a variable and 0 is same as the variable itself. Likewise, multiplication of the variable with 1 is same as the variable itself. i.e.,➡ A + 0 = A➡ A.1= AProof: Hence, A + ...

Laws of Boolean Algebra

# Boolean PostulatesAccording to Boolean Postulates of Boolean Algebra, OR law AND law NOT law A + 0 = A A.1 = A 0' = 1 A + 1 = 1 A.0 = 0 1' = 0 A + A= A A.A = A A'' = A A + A' = 1 A.A' = ...

Derived Logic Gates

#NAND gateIt is the combination of AND and NOT gates which produces low output when all inputs are high, otherwise the output will be high. It is the integration of NOT gate and AND gate that means...

Basic Logic Gates

# AND gate/ Logical AND→It is an electronic circuit used to perform logical multiplication(or AND operation) which is denoted by dot operator(.). So, its Boolean Expression is "A.B". It produces hi...

Boolean Algebra - Introduction

Introduction The algebra of logic, which deals with the study of binary variables and logical operations, and also manipulates them is known as Boolean Algebra. This makes it possible to tr...

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