This document discusses how digital data is represented and stored using binary numbers in computers. It explains that binary uses only 1s and 0s, with each binary digit called a bit. 8 bits make a byte, which can represent 256 combinations. Bytes can store numbers, letters, images and other digital data. The document provides examples of how binary numbers represent decimal numbers and how binary is used to store RGB color codes in hexadecimal format.

1. S
CSC 103
Bits & Bytes
The Language of Computers

2. Digital Data (Bits & Bytes)
 Data on a computer text, numbers &
pixels are stored and represented digitally.
 Digital Data is read in bits and bytes
by computers processors.
 Bits and Bytes make up the binary
language.

3. Binary Language
 The language of computers is binary.
 Uses series of 1’s and 0’s –
which represent on/off state.
 Used for giving instructions.
 Also used for measuring the quantity
or storing data.

4. Example of Binary
 Morse Code (in 1844) was sent with
electrical impulses over a wire which
translated to dots and dashes (a form of
binary code) to create messages
heard by the human ear.
 Evolved into telegraph/telegram messages.

5. Binary Digit (Bit)
 1’s and 0’s are binary digits
 Bit is short for binary digit
 1 bit can only be 1 or 0…
so it is expanded to 8 bits
or 1 byte (28) which allows
for 256 combinations
of 1’s and 0’s

6. Binary Combinations
Combinations will continue to double
512, 1024, 2048…

7. 1 Byte = 8 Bit
 8 bits = 1 Byte which represents enough
numbers to convert to ASCII letters
(or characters) of the alphabet.
 1000 bytes – kilobyte
 1,000,000 (million) bytes – megabyte
 1,000,000,000 (billion) bytes - gigabyte

8. Bits translated to Numbers
 Binary can represent numbers
higher than 0 and 1.
 Instead of 1’s, 10’s, 100’s, 1000’s etc.,
like our base 10 number system,
it uses binary or base 2.
 It uses 1’s, 2’s, 4’s, 8’s, 16’s, 32’s, 64’s, etc.
(starting from right (1’s) to left)

9. Our Base-10 System
(Decimal)
1 0 1 1
1000’s 100’s 10’s 1’s
1000 + 0 + 10 + 1
= 1,011

10. Our Base-10 System
(Decimal)
9 4 7 0
1000’s 100’s 10’s 1’s
9000 + 400 + 70 + 0
= 9,470

11. Our Base-10 System
(Decimal)
0 4 7 0
1000’s 100’s 10’s 1’s
0 + 400 + 70 + 0
= 470

12. Bits converted to Numbers
4-bit example
1 0 1 1
8’s 4’s 2’s 1’s
8 + 0 + 2 + 1
8 + 3 + 1 = 11 (value)

13. Bits converted to Numbers
4-bit example
1 1 1 1
8’s 4’s 2’s 1’s
8 + 4 + 2 + 1
8 + 4 + 2 + 1 = 15 (value)

14. Bits converted to Numbers
4-bit example
1 0 1 0
8’s 4’s 2’s 1’s
8 + 0 + 2 + 0

15. Bits converted to Numbers
4-bit example
__ __ __ __
8’s 4’s 2’s 1’s
What binary number = 9

16. Bits converted to Numbers
4-bit example
1 0 0 1
8’s 4’s 2’s 1’s
8 + 0 + 0 + 1 = 9

17. Bits converted to Numbers
8-bit example
1 0 1 0
8’s 4’s 2’s 1’s
128 + 0 + 32 + 0 + 8 + 0 + 2 + 0
160 + 10 = 170 (value)
1 0 1 0
128’s 64’s 32’s 16’s

18. Bits converted to Numbers
8-bit example
1 1 1 1
8’s 4’s 2’s 1’s
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
240 + 15 = 255
1 1 1 1
128’s 64’s 32’s 16’s

19. Bits converted to Numbers
8-bit example
0 0 0 0
8’s 4’s 2’s 1’s
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1
0 + 0 = 0
0 0 0 0
128’s 64’s 32’s 16’s

20. Shortcut to Count 8-bit
Count each side up to 15
1 1 1 1
8’s 4’s 2’s 1’s
8 + 4 + 2 + 1 8 + 4 + 2 + 1
240 + 15 = 255
1 1 1 1
128’s 64’s 32’s 16’s
15 * (1)15 * (16)

21. Shortcut to Count 8-bit
Count each side up to 15
0 1 1 1
8’s 4’s 2’s 1’s
8 + 0 + 0 + 1 + 0 + 4 + 2 + 1
9 7
1 0 0 1
__ * (1)__ * (16)
8’s 4’s 2’s 1’s

22. Shortcut to Count 8-bit
Count each side up to 15
0 1 1 1
8’s 4’s 2’s 1’s
8 + 0 + 0 + 1 + 0 + 4 + 2 + 1
144 + 7 = 151
1 0 0 1
7 * (1)9 * (16)
8’s 4’s 2’s 1’s

23. Shortcut to Count 8-bit
What binary number is 160?
0 0 0 0
8’s 4’s 2’s 1’s
0 + 0 + 0 + 0 + 0 + 0 + 0 + 0
0 + 0 = 0
0 0 0 0
__ * (1)__ * (16)
8’s 4’s 2’s 1’s

24. Shortcut to Count 8-bit
What binary number is 160?
160 / 16 = _____
Remainder is the 1’s ________
__ * (1)__ * (16)

25. Shortcut to Count 8-bit
What binary number is 160?
160 / 16 = 10
Remainder is the 1’s: 0
0 * (1)10 * (16)

26. Shortcut to Count 8-bit
What binary number is 160?
0 0 0 0
8’s 4’s 2’s 1’s
8 + 0 + 2 + 0 + 0 + 0 + 0 + 0
160 + 0 = 160
1 0 1 0
0 * (1)10 * (16)
8’s 4’s 2’s 1’s

27. Shortcut to Count 8-bit
This is essentially the Hexadecimal System
0 0 0 0
8’s 4’s 2’s 1’s
8 + 0 + 2 + 0 + 0 + 0 + 0 + 0
160 + 0 = 160
1 0 1 0
0 * (1)10 * (16)
8’s 4’s 2’s 1’s

28. RGB Color translated to
Hexadecimal Color
 Hexadecimal Color is used to describe
RGB color on web pages.
 It uses 16’s and 1’s (in 2-digits) but
uses letters to represent 10-15
For Example:
 RGB: 255 255 255
(white – highest number)
 Hex: #FF FF FF or #FFF

29. Credits
 www.mathisfun.com
 introcomputing.org
 sticksandstones.kstrom.com
 e-tutes.com
 Richard Homa ©2019