UNIVERSITY OF MYSORE MANASAGANGOTHRI

SECOND SEMESTER

Paper : Fundamentals of Information TechnologySeminar on :Binary Numbers addition subtraction

multiplication division

Presented to,Dr.Chandrashekar .MProfessorDOS in Library and Information ScienceManasagangothri, Mysore

Presented byKanthamani H D

Contents

Introduction Definition Some Binary Arithmetic Addition Subtraction◦ Signed magnitude numbers◦ 2’s complement numbers Multiplication Division

Introduction:-The binary number system is used in the

computer systems. The digits 0 and 1 are combined to get different binary numbers like 1001, 11000110 etc. In a binary number, a digit 0 or 1 is called a bit. For example, 1001 is a 4-bit binary number, and, 11000110 is an 8-bit binary number. All kinds of data, be it alphabets, numbers, symbols, sound data or video data, are represented as combination of bits i.e. 0’s and 1’s. Each character is a unique combination of bits. We shall now discuss how to perform basic arithmetic operations in the binary number system.

Definition:- A binary is a system in which the number system has

a number 2 as it's base. It can also pertain to a binary star which is a system of 2 stars.

or Binary a numbering system that is also the

language spoken by computers. It is made up of only 0s and 1s. For example, the number 37 in binary is 100101.

Binary Number System:-

 Binary is the language of computers. Information is sent to and from the processor in the binary system which consists of only two digits (1 and 0). For example a line of ones and zeros eight digits long can represent up to 256 different values that

Addition Subtraction ◦ Signed magnitude numbers ◦ 2’s complement numbers Multiplication Division

Some Binary Arithmetic

Binary addition is performed in the same manner as decimal addition. However, since binary system has only two digits, the addition table for binary arithmetic is very simple consisting of only four entries. The complete table for binary addition is as follows.

Rules of Binary Addition 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 0, and carry 1 to the next more significant

bit

Binary Addition

Examples :Add the binary numbers 1011 and 1001.              1011            + 1001            10100 Add the binary numbers 100111 and 11011.               100111             +  11011             1000010

00011010 + 00001100 = 00100110

0 0 0 1 1 0 1 0 = 26(base 10)

+ 0 0 0 0 1 1 0 0 = 12(base 10)

0 0 1 0 0 1 1 0 = 38(base 10)

00010011 + 00111110 = 01010001 1 1 1 1 1 carries

0 0 0 1 0 0 1 1 = 19(base 10) + 0 0 1 1 1 1 1 0 = 62(base 10) 0 1 0 1 0 0 0 1 = 81(base 10)

Binary Subtraction The principles of decimal subtraction can as

well be applied to subtraction of numbers in other cases. It consists of two steps, which are repeated for each column of the numbers. The first step is to determine if it is necessary to borrow. 

Rules of Binary Subtraction 0 ‐ 0 = 0 0 ‐ 1 = 1, and borrow 1 from the next more significant bit 1 ‐ 0 = 1 1 ‐ 1 = 0

For example:-00100101 ‐ 00010001 = 00010100

0 borrows 0 0 10 0 1 0 1 = 37(base 10) 0 0 0 1 0 0 0 1 = 17(base 10) 0 0 0 1 0 1 0 0 = 20(base 10)

Complement of Binary Numbers:-Complements are used in computer

for the simplification of the subtraction operation. We now see, how to find the complement of a binary number. There are two types of complements for the binary number system – 1’scomplement and 2’scomplement.

1’s complement of Binary number is computed by changing the bits 1 to 0 and the bits 0 to 1.

For example,1’s complement of 110 is 001 1’s complement of 1011 is 0100 1’s complement of 1101111 is 0010000

2’s complement of Binary number is computed by adding 1 to the 1’s complement of the binary number.

For example:-2’s complement of 110 is 001 + 1 = 010 2’s complement of 1011 is 0100 + 1 = 0101 2’s complement of 1101111 is 0010000 + 1 =

00100011 1 0 10110 0 1 0100 + 1 + 10 1 0 0101

Binary Multiplication The multiplication of two binary

numbers can be carried out in the same manner as the decimal multiplication.

Unlike decimal multiplication, only two values are generated as the outcome of multiplying the multiplication bit by 0 or 1 in the binary multiplication. These values are either 0 or 1.

The binary multiplication can also be considered as repeated binary addition. Therefore, the binary multiplication is performed in conjunction with the binary addition operation.

Rules of Binary Multiplication 0 x 0 = 0   0 x 1 = 0   1 x 0 = 0   1 x 1 = 1, and no carry or borrow bitsFor example

1 1 0 0*1 0 1 0 1 1 0 0

0 0 0 0 11 0 0 0 0 0 0 0 1 1 1 1 0 0

     

1 0 1 0 * 1 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 0

Binary division is also performed in the same way as we perform decimal division. Like decimal division, we also need to follow the binary subtraction rules while performing the binary division. The dividend involved in binary division should be greater than the divisor. The following are the two important points, which need to be remembered while performing the binary division.

• If the remainder obtained by the division process is greater than or equal to the divisor, put 1 in the quotient and perform the binary subtraction.

Binary Division

If the remainder obtained by the division process is less than the divisor, put 0 in the quotient and append the next most significant digit from the dividend to the remainder.

Binary Division Binary division is the repeated process of subtra

ction, just as in decimal division.For example

1 1 0)0 0 1 0 1 0 1 0 (1 1 1

1 1 0 1 0 0 1 1 1 0 0 0 1 1 0 1 1 0 0 0 0

Conclusion:-The binary number system, base two, uses

only two symbols, 0 and 1. Two is the smallest whole number that can be used as the base of a number system. For many years, mathematicians saw base two as a primitive system and overlooked the potential of the binary system as a tool for developing computer science and many electrical devices.

Base two has several other names, including the binary positional numeration system and the dyadic system. Many civilizations have used the binary system in some form, including inhabitants of Australia, Polynesia, South America, and Africa. Ancient Egyptian arithmetic depended on the binary system.