10th Class Computers Science Classification of Computer and Number System Binary Addition

   Binary Addition

The addition rules for binary bits are:

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1                                                                                .

1 + 1 = 10

1 + 1 + 1 = 11    

 One's Complement

One's component is a system that is used to represent negative numbers. To take 1's complement of binary digit, replace all Is with Os and all Os with Is. For Example, 1's complement of 111111 is 000000.  

  Two's Complement

While taking two's complement of a binary number you need to first obtain the first complement of that number then add 1 in the 1's complement. The following example shows how to find 2's complement of 111110.

1's complement of 111110 is 000001.

Adding 1 in the 1's complement:

000001

+1

000010  

  Which one of the following statements is true? Statement A: The octal number system is based on 8. Statement B: 998 is an octal number.

(A) Statement A is correct                           

(B) Statement B is correct

(C) Both statement A and B are correct  

(D) Neither statement A nor statement B is correct  

Answer: (a)

Explanation

Correct Option:

(A) Only statement a is correct.

Incorrect Options:

Therefore, option (A) is correct and rest of the options is incorrect.  

  One's component is a system that is used to represent negative numbers. The one's complement of 111000 is ...............

(A) 000111                                                          

(B) 001111

(C) 110011                                                          

(D) 010011

(E) None of these  

Answer: (a)

Explanation

Correct Option:

(A) The ones's complement of 111000 is 000111.

Incorrect Options:

Therefore, option (A) is correct and rest of the options is incorrect.  

  While taking two's complement of a binary number you need to first obtain the first complement of that number. The two's complement of 111111 is ...............

(A) 000000                                                          

(B) 100000

(c) 000001                                                           

(D) 111111

(E) None of these  

Answer: (c)

Explanation

Correct Option:

(C) 1's complement of 111111 is 000000. Adding 1 in the 1's complement: 000000 +1 000001

Incorrect Options:

Therefore, option (C) is correct and rest of the options is incorrect.  

• In 17th century the modern binary number system was fully documented by Gottfried Leibniz.  

• Binary Number: The whole binary number system depends on two digits these are 0 and 1, respectively.
• Binary Addition: 1 + 1 + 1 = 11  

• Whole binary number system depends on the two basic digits
• The place value in hexadecimal system is increased in the power of 16 from right to left. The place value of a digit in a number increases in the power of 8 from right to left.
• To convert octal into binary you need to convert each octal digit to its 3-bit binary equivalent.
• While taking two's complement of a binary number you need to first obtain the first complement of that number then add 1 in the 1's complement. v  A system with base-10 is a decimal number system.
• The hexadecimal number system is based on 16. The whole octal number system is based on 8.