Binary

Binary numbers

• Every piece of data in our computer can be represented by Ones and Zeros

• Each one or zero is called a “bit” and represents the smallest cell in a computer’s memory

• You can think of a bit as an On/Off switch – a bit is either 1 or 0 (on or off / true or false)

• Bit - shorthand for binary digit.

• Binary digit - either 0 or 1.

• Binary base - uses only combinations of the digits zero

and one.

• Byte - 8 bits.

Vocab

• A byte is how much a computer likes to "bite" at once

• The byte is also the smallest addressable unit of memory in most

modern computers

• In other words, a computer with byte-addressable memory can NOT

store an individual piece of data that is smaller than a byte

Answer

• Even though computers "bite" 8 bits of data a time, they can

also "nibble"

• When a computer "nibbles" it is processing 4 of the 8 bits

How does the
Decimal
System work?

When we write the
number 872, what do
we mean?

8

7

2

100’s
place

10’s
place

1’s

place

8 x 100
= 800

7 x 10 =

70

2 x 1 =

2

800 + 70 + 2 = 872

Binary number system

Decimal system:

0 – 9

10,000’s

place
(10⁴)

1,000’s
place
(10³)

100’s place

(10²)

10’s place

(10¹)

1’s place

(100)

Binary system:
0,1

16’s place

(2⁴)

8’s place

(2³)

4’s place

(2²)

2’s place

(2¹)

1’s place

(20)

Converting Decimal to Binary

Decimal
number:

Binary
number:

8

1

0

0

0

8’s
plac

e

4’s
plac

e

2’s
plac

e

1’s
plac

e

1 x
8 =
8

0 x
4 =
0

0 x
2 =
0

0 x
1
= 0

8 + 0 + 0 + 0 = 8

7

0

1

1

1

8’s

place

4’s

place

2’s

place

1’s

place

0 x 8
= 0

1 x 4
= 4

1 x 2
= 2

1 x 1
= 1

0 + 4 + 2 + 1 = 7

Converting Decimal numbers to Binary
numbers
• Draw an underline as a placeholder for each of the bits.
• Underneath each line, write the binary placeholder value (base 2).

Converting Decimal numbers to Binary
numbers
•Is the number greater than or equal to this place value?

⚬ If yes, then write a 1 above the line

and subtract the place value from the decimal number

⚬ If no, then write a 0 above the line

•Repeat until decimal number is 0

Let’s practice!

•Is the number greater than or equal to this place value?

⚬If yes,

then write a 1 above the line

and subtract the place value from the decimal number

⚬If no, then write a 0 above the line

•Repeat until decimal number is 0

Practice with random numbers

•Go to random.org

•Choose the Random Integer generator

•Generate three random integers from 0-255

•Get numbers

•As you practice converting your random numbers, write each step out

Is 231 > 128? Yes. Write 1 above 128. 231-128=103

Is 103 > 64? …

1 bit pattern?

Decimal

Binary

1

00000001

3

00000011

7

00000111

15

00001111

Bits (
1
2
3
4

Next number?

Bits (

Decimal

Binary

5

31

6

63

7

127

8

255

Bits (

Decimal

Binary

5

31

00011111

6

63

00111111

7

127

01111111

8

255

11111111

Bytes…

Where have you seen them in

everyday life?

Image of files

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