Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

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# Binary Adding, Subtraction, Multiplicaton and Division

A binary signal or number is one that can take only one value: 1 or 0 -or on or off.

• 0 + 0 = 0
• 0 + 1 = 1
• 1 + 0 = 1
• 1 + 1 = 0 (with a carry of 1)

DecimalBinary
1 5
+ 6
= 11
101
+ 110
= 1011
2 6
+ 6
= 12
110
+ 110
= 1100
3 15
+ 20
= 35
1111
+ 10100
= 100011
4 3.25
+ 5.75
= 9.00
11.01
+ 101.11
= 1001.00

### Subtracting Binary Numbers

Rule to follow when binary numbers are subtracted:

• 0 - 0 = 0
• 1 - 0 = 1
• 1 - 1 = 0
• 0 - 1 = 1 (with a borrow of 1)

#### Examples - Subtracting Binary and Decimal Numbers

Subtracting Binary and Decimal Numbers
DecimalBinary
1 9
- 5
= 4
1001
- 101
= 0100
2 16
- 3
= 13
10000
- 11
= 01101
3 6.25
- 4.50
= 1.75
110.01
- 100.10
= 001.11

### Multiplication of Binary Numbers

Rule to follow when binary numbers are multiplied:

• 0 x 0 = 0
• 0 x 1 = 0
• 1 x 0 = 0
• 1 x 1 = 1

### Division of Binary Numbers

Rule to follow when binary numbers are divided:

• 0 / 1 = 0
• 1 / 1 = 1

## Related Topics

### • Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

## Related Documents

### Binary to Decimal, Hexadecimal and ASCII Converter

Convert between binary, decimal and hexadecimal numbers.

### Binary, Octal and Hexadecimal Numbers

Decimal, binary, octal and hexadecimal numbers.

### Decimal System Prefixes

Prefix names used for multiples and submultiples units.

### Prefixes for Binary Multiplies

IEC International Standard names and symbols

### Scientific Calculator

Online scientific calculator.

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