Binary

• We use computers every day

• Inside a computer are “0s and 1s”

  • Computers use the binary number system to represent info
    • How do computers represent info with just binary?

• Consider the decimal number (what we humans typically use) 123

  • The rightmost column is the 1s column

  • The middle, the 10s

  • The leftmost, the 100s

    100	10	1
    1	2	3

  • Thus we have 100 x 1 + 10 x 2 + 1 x 3 = 100 + 20 + 3 = 123

• Inside a computer, the binary 000 would represent 0, just like in our human world!

  • However, in this case, we are dealing with binary so:

    • The right-most column is the 1s place
    • The middle, the 2s
    • The leftmost, the 4s

    4	2	1
    0	0	0

  • In the human world (decimal) we use powers of 10 for place values

    • 10 = 1, 10 = 10, 10 = 100, 10 = 1000, etc.

      0

      1

      2

      3

  • In the computer world (binary) we use powers of 2 for place values

    • 2 = 1, 2 = 2, 2 = 4, 2 = 8, etc.

      0

      1

      2

      3

  • The difference between decimal numbers and binary numbers is changing the base

  • For the binary number 000, we have 4 x 0 + 2 x 0 + 1 x 0 = 0 + 0 + 0 = 0!

• Consider the binary number 001:

  4	2	1
  0	0	1

  • We have 4 x 0 + 2 x 0 + 1 x 1 = 0 + 0 + 1 = 1

• How do we represent the decimal number 2 in binary?

  • We don’t need a 4, be we need a 2, and also no 1

  4	2	1
  0	1	0

  • This gives us 4 x 0 + 2 x 1 + 1 x 0 = 0 + 2 + 0 = 2

• Likewise, the number 3 would be:

  4	2	1
  0	1	1

  • As we need a 2 and a 1
  • Thus, 4 x 0 + 2 x 1 + 1 x 1 = 0 + 2 + 1 = 3

• Similarly, 4 would be:

  4	2	1
  1	0	0

• What about 7?

  What about 7?

  4	2	1
  1	1	1

  • Which yields 4 x 1 + 2 x 1 + 1 x 1 = 4 + 2 + 1 = 7

• What about 8?

  • We can’t count to 8 without another bit (binary digit)

    • We run into this in the real world too if we need a four-digit number vs a 3-digit number
      • Start with the 1s, 10s, 100s place and add the 1000s
    • Here we’ll add the next power of 2, 8

    8	4	2	1
    1	0	0	0

    • 8 x 1 + 4 x 0 + 2 x 0 + 1 x 0 = 8

• Even though computers only use binary, they can count as high as humans can!

  • They do it with a smaller vocabulary, just 1 and 0.
    • This is because it’s easier to represent two states in the physical world
      • If you think of one of these bits as being a light bulb:
        • 0 is off
        • 1 is on
      • Light bulbs just need electricity to turn on or off
      • Electricity is sufficient to turn a switch on or off
        • Inside a computer exist these switches called transistors
          • Modern computers have billions!
          • Turned off represents 0
          • Turned on represents 1

• Using these transistors we can store values, store data, compute, and do everything we can with computers

• David demonstrates how transistors work using light bulbs

• So far all that we can represent our numbers

• Consider this pattern of bits: 01001000 01001001

CPU

• If you have heard that your computer has “Intel Inside,” it has an Intel processor in it
• The CPU is the brain of the computer
• CPUs now can have multiple cores