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.

5 10 ->

101 2

1210 = C16

11002 = 12

10

Converting from base 10 (decimal)to base 2 (binary) example number = 42

3. Write a 1 underneath if that place value is used, 0 if not. subtract to find out what is left.

Read your answer from left to rightThe number in binary is 101010

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

DEMONSTRATE

Watch

12481632641 0 1 0 1 0

42

-32

----

10

10

- 8

----

2

2

-2

----

0

This is too big

Converting from base 10 (decimal)to base 2 (binary) example number = 7053

the number in binary is 1101110001101

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

DO TOGETHER

Do this together

12481632641282565121024204840968192

1

7053

-4096

-------

2957

1

2957

-2048

-------

909

0 1

909

- 512

-------

397

1

397

-256

------

141

1

141

-128

-------

13

0 0 0 1

13

- 8

-----

5

1

5

-4

---

1

1

1

-1

---

0

0Too

big

Do this one 15010 binary

124816

32

64

128

256

The answer is: 10010110

STUDENT’S TURN

1 0 0 1 0 1 1 0Click to see each digit that is needed.

Too big

To convert binary to decimal Write the powers of 2 below each digit and only add the values with a 1 above them.

the number in binary is 10111001101

1 0 1 1 1 0 0 1 1 0 1

1024 512 256 128 64 32 16 8 4 2 1

Watch

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

Start at the right and double each number

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?

The answer is: 101001

64 32 16 8 4 2 1

1 0 1 0 0 1

Quick Review: binary to decimal

10011012 decimal 64 + 8 + 4 + 1 =77

An Introduction toHexadecimal 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 to hexadecimal) 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

example number = 7053

Watch

Do this one

96210 hexadecimal

3C216

This is 3*256 + C(10)*16 + 2

from hexadecimal (base 16) back to decimal 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

1B8D16

1162564096

Watch

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 to octal) 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

example number = 7053

Watch

Do this one:

94610 octal

16628

from octal (base 8) back to decimal

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

added together = 7053

156158

Watch

Do this one

20458

106110

Binary hex octal

If you can count from 1 to 15 in binary you have it made

0

1

10

11

100

101

110

111

1000

1001

1010

1011

1100

1101

1110

1111

Binary to hexadecimal and hex to binary 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

Binary Hexadecimal

11 0101 1110

3 5 E

35E16

Hex Binary

28D1

10 1000110100012

Watch

Write this down the side of your paper.

Practice Hex Binary Hex

Convert E5816 to Binary111001011000

Convert 110010110 to Hexadecimal196

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

100101001 Watch

Practice Octal Binary Octal

Convert 3078 to Binary11000111

Convert 110010110 to Octal646

octal to hex and hex to octal.

Convert to binary, regroup and convert to other base.

Octal to binary to hex4518

100 101 001

100101001

1 0010 100112916

Watch

Practice Octal Hex

Convert 3078 to Hex11 000 111 first in binary110001111100 0111 divide into groups of 4 12 7C716

Practice Hex Octal

Convert 2B1D16 to Octal10 1011 0001 1101 first in binary10101100011101 10 101 100 011 101 divide into groups of 3 2 5 4 3 5254358

The End