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## PowerPoint Slideshow about ' Number Systems' - maeko

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Objectives

- Understand the concept of number systems.
- Describe the decimal, binary, hexadecimal and octal system.
- Convert a number in binary, octal or hexadecimal to a number in the decimal system.
- Convert a number in the decimal system to a number in binary, octal and hexadecimal.
- Convert a number in binary to octal, hexadecimal and vice versa.

The decimal system

- Base: 10
- Decimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
- Examples:

The binary system

- Base: 2
- Decimal digits: 0, 1
- Examples:

The hexadecimal system

- Base: 16
- Hexadecimal digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F
- Examples:

The octal system

- Base: 8
- Decimal digits: 0, 1, 2, 3, 4, 5, 6, 7
- Examples:

Binary to Decimal

- Technique
- Multiply each bit by 2n, where n is the “weight” of the bit
- The weight is the position of the bit, starting from 0 on the right
- Add the results

Octal to Decimal

- Technique
- Multiply each bit by 8n, where n is the “weight” of the bit
- The weight is the position of the bit, starting from 0 on the right
- Add the results

Example

7248 => 4 x 80 = 4 2 x 81 = 16 7 x 82 = 448 46810

Hexadecimal to Decimal

- Technique
- Multiply each bit by 16n, where n is the “weight” of the bit
- The weight is the position of the bit, starting from 0 on the right
- Add the results

Decimal to Binary

- Technique
- Divide by two, keep track of the remainder
- First remainder is bit 0 (LSB, least-significant bit)
- Second remainder is bit 1
- Etc.

Decimal to Octal

- Technique
- Divide by 8
- Keep track of the remainder

Decimal to Hexadecimal

- Technique
- Divide by 16
- Keep track of the remainder

Octal to Binary

- Technique
- Convert each octal digit to a 3-bit equivalent binary representation

Hexadecimal to Binary

- Technique
- Convert each hexadecimal digit to a 4-bit equivalent binary representation

Binary to Octal

- Technique
- Group bits in threes, starting on right
- Convert to octal digits

Binary to Hexadecimal

- Technique
- Group bits in fours, starting on right
- Convert to hexadecimal digits

Octal to Hexadecimal

- Technique
- Use binary as an intermediary

Hexadecimal to Octal

- Technique
- Use binary as an intermediary

Exercise – Convert ...

Summary of Conversion Methods

Binary Addition (2 of 2)

- Two n-bit values
- Add individual bits
- Propagate carries
- E.g.,

1

1

10101 21+ 11001 + 25 101110 46

Multiplication (1 of 2)

- Binary, two 1-bit values

Multiplication (2 of 2)

- Binary, two n-bit values
- As with decimal values
- E.g.,

1110 x 1011 1110 1110 0000 111010011010

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