Number systems

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# Number systems - PowerPoint PPT Presentation

Number systems. Converting numbers between binary, octal, decimal, hexadecimal (the easy way). Small numbers are easy to convert. But it helps to have a system for converting larger numbers to avoid errors. 12 10 = C 16. 5 10 -> 101 2. 1100 2 = 12 10. DEMONSTRATE.

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## Number systems

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### Number systems

Converting numbers between binary, octal, decimal, hexadecimal

(the easy way)

Small numbers are easy to convert
• But it helps to have a system for converting larger numbers to avoid errors.

1210 = C16

510 -> 1012

11002 = 1210

DEMONSTRATE

Converting from base 10 (decimal)to base 2 (binary)

example number = 42

• Write the powers of 2 in a row starting on the RIGHT side with a 1
• Keep doubling (*2) until you get to something greater than your number (42)

64

32

16

8

4

2

1

This is too big

1

0

1

1

3. Write a 1 underneath if that place value is used, 0 if not.

subtract to find out what is left.

0

0

42

-32

----

10

10

- 8

----

2

2

-2

----

0

Watch

The number in binary is 101010

DO TOGETHER

Converting from base 10 (decimal)to base 2 (binary)

example number = 7053

• write the powers of 2 in a row until you get to something > the number

8192

4096

2048

1024

512

256

128

64

32

16

8

4

2

1

Too

big

0

1

1

0

1

1

1

0

0

0

1

1

1

7053

-4096

-------

2957

2957

-2048

-------

909

909

- 512

-------

397

397

-256

------

141

141

-128

-------

13

13

- 8

-----

5

5

-4

---

1

1

-1

---

0

Do this together

the number in binary is 1101110001101

STUDENT’S TURN

Do this one 15010 binary
• 1
• 2
• 4
• 8
• 16
• 32
• 64
• 128
• 256

1

0

Too big

1

0

0

1

0

1

Click to see each digit that is needed.

To convert binary to decimal

the number in binary is 10111001101

• Write the powers of 2 below each digit and only add the values with a 1 above them.
• 0 1 1 1 0 0 1 1 0 1
• 1024 512 256 128 64 32 16 8 4 2 1

Start at the right and double each number

1024 + 256+128+64 + 8 + 4 + 1 = 1,485

Watch

Your turn. Convert 1000100112 to decimal
• 1 0 0 0 1 0 0 1 1
• 256 128 64 32 16 8 4 2 1
• 256 + 16 + 2+1 =
• 275
• …. And now, for more about number systems.
Part 2
• Number Systems
Quick review
• What’s 41 in binary?
• 32 16 8 4 2 1
• 1 0 1 0 0 1

Quick Review: binary to decimal
• 10011012 decimal
• 64 + 8 + 4 + 1
• =77
• 16 digits
• Use letters when you run out of single digits
• 0 1 2 3 4 5 6 7 8 9 A B C D E F
• SO… 1110 = ?16
• B16
• 1510 = ?
• F16
• 1610 = ?
• 1016
from base 10 to base 16 (decimal tohexadecimal)

example number = 7053

• write the powers of 16 in a row until you get to one > the number
• divide the number by each power of 16 and write the answer and save the remainder

65,536 4,096 256 16 1

• Too high
• 7053/4096 = 1 R 2957
• 2957/256 = 11 R 141
• 141/16 = 8 R 13
• 13 ones
• the numbers in hex are:
• 1 2 3 4 5 6 7 8 9 A B C D E F (A=10…. F=15)
• So your number is 1 11 8 13 = 1B8D16

Watch

Do this one
• 3C216
• This is 3*256 + C(10)*16 + 2
from hexadecimal (base 16) back to decimal

Watch

1B8D16

• Write the number across a row. Write the powers of 16 below it. Multiply. Then add the products.
• 1 B 8 D
• =(1X4096)+
• (11*256)+
• (8*16)+(13*1) =
• 4096 + 2816 + 128 + 13 = 7053

4096

256

16

1

Do this one
• A10E16 decimal
• 41230
Octal
• Base 8
• Uses 8 different digits
• 0 1 2 3 4 5 6 7
from base 10 to base 8(decimal tooctal)

example number = 7053

• write the powers of 8 in a row until you get to one > the number
• divide the number by each power of 8
• write the answer and save the remainder
• 32768 4096 512 64 8 1
• too high
• 7053/4096 = 1 R 2957
• 2957/512 = 5 R 397
• 397/64 = 6 R 13
• 13/8 = 1 R 5
• = 5 ones
• so your number in octal is 156158

Watch

Do this one:
• 94610 octal
• 16628
from octal (base 8) back to decimal

156158

• write the number
• write the powers of 8 below it and multiply. then add the products.
• 1 5 6 1 5
• 4096 512 64 8 1
• 1 *4096 = 4096
• 5 * 512 = 2560
• 6 * 64 = 384
• 1* 8 = 8
• 5 * 1 = 5

Watch

Do this one
• 20458
• 106110

0

1

10

11

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

Binary  hex  octal
• If you can count from 1 to 15 in binary you have it made
Binary to hexadecimal and hex to binary

Watch

• 4 binary digits correspond to 1 hexadecimal digit
• Start grouping digits on the RIGHT side
• 0000 0
• 0001 1
• 0010 2
• 0011 3
• 0100 4
• 0101 5
• 0110 6
• 0111 7
• 1000 8
• 1001 9
• 1010 A
• 1011 B
• 1100 C
• 1101 D
• 1110 E
• 1111 F

To convert binary 1101011110 to hex

11 0101 1110

3 5 E

35E16

Write this down the side of your paper.

Hex  Binary

28D1

10 1000110100012

Practice Hex  Binary  Hex
• Convert E5816 to Binary
• 111001011000
• 196
binary to octal and octal to binary
• 3 binary digits correspond to 1 octal digit
• 000 0
• 001 1
• 010 2
• 011 3
• 100 4
• 101 5
• 110 6
• 111 7

Binary to octal

10110011

10 110 011

263

• Octal to binary
• 451
• 100 101 001
• 101001

Watch

Practice Octal  Binary  Octal
• Convert 3078 to Binary
• 11000111
• Convert 110010110 to Octal
• 646
octal to hex and hex to octal.
• Convert to binary, regroup and convert to other base.

Octal to binary to hex

4518

100 101 001

100101001

1 0010 1001

12916

Watch

Practice Octal  Hex
• Convert 3078 to Hex
• 11 000 111 first in binary
• 11000111
• 1100 0111 divide into groups of 4
• 12 7
• C716
Practice Hex  Octal
• Convert 2B1D16 to Octal
• 10 1011 0001 1101 first in binary
• 10101100011101
• 10 101 100 011 101 divide into groups of 3
• 2 5 4 3 5
• 254358