Binary Arithmetic and Conversion
You have to learn addition, subtraction, multiplication, and division of binary number. In brain, you have to keep that in the arithmetic of binary number, carry is written in binary (2) just like as 10 is used in decimal system for carry. This note provides an information about binary arithmetic.
Summary
You have to learn addition, subtraction, multiplication, and division of binary number. In brain, you have to keep that in the arithmetic of binary number, carry is written in binary (2) just like as 10 is used in decimal system for carry. This note provides an information about binary arithmetic.
Things to Remember
- To convert decimal number to binary number, repeated division by two is needed.
- To convert binary to decimal number system, multiply given number by 2.
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Binary Arithmetic and Conversion
Conversion from Decimal to Binary
To convert the decimal number to binary number, repeated division by two is needed.
Examples: Convert following into binary numbers:
- (45)10= (101101)2
2 45 1 2 22 0 2 11 1 2 5 1 2 2 0 1 =(101101)2
- (225)10= (10111001)2
2 225 1 2 112 0 2 56 0 2 23 1 2 11 1 2 5 1 2 2 0 1 = (10111001)2
Conversion from Binary to Decimal
To convert binary to the decimal number system, multiply given number by 2.
1. (1101)2=(?)10
=1x23+ 1 x 22+ 0x 21+ 1x 20
=8 + 4 + 0 + 1
=13
Rules for Binary Addition
| A | B | A+B |
| 0 | 0 | 0 |
| 0 | 1 | 1 |
| 1 | 0 | 1 |
| 1 | 1 | 0 with carry 1 |
- 1100 + 1111= 11011
1 Carry 1 1 0 0 1 1 1 1 11 0 1 1
Rules for Binary Multiplication
| A | B | A*B |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 0 |
| 1 | 1 | 1 |
Lesson
Number System
Subject
Computer
Grade
Grade 8
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