Post on 04-Jan-2016
What are these?What are these?
Binary ClockBinary Clock
ICE3MICE3M
May 7, 2007May 7, 2007
Ms. NelsonMs. Nelson
Telling Time in BinaryTelling Time in Binary
1 or 0
2 or 0
4 or 08 or 0
16 or 032 or 0
1 + 4 + 8 + 32 = 45 seconds!
Similarly, the clock is currently showing
4 + 8 = 12 for the hour, and
4 + 2 + 1 = 7 for the minutes
Therefore the current time is 12:07 and 45 seconds.
Computers and StorageComputers and Storage
Everything inside your computer is boiled Everything inside your computer is boiled down to tiny on/off switchesdown to tiny on/off switches
Traditionally, we use 0 for off and 1 for onTraditionally, we use 0 for off and 1 for on Ever noticed this on on/off switches?Ever noticed this on on/off switches?
Numbers are stored this way tooNumbers are stored this way too
Counting with 0’s and 1’sCounting with 0’s and 1’s
Pretend we only had 0’s and 1’s to work Pretend we only had 0’s and 1’s to work with, and not 2, 3, 4, 5, 6, 7, 8, 9.with, and not 2, 3, 4, 5, 6, 7, 8, 9.
How many numbers can you come up How many numbers can you come up with?with? 0, 1, 10, 11 (but not 12, 13, 14… have to 0, 1, 10, 11 (but not 12, 13, 14… have to
skip all the way up to 99)skip all the way up to 99) 100, 101, 110, 111100, 101, 110, 111 1000…. 1000…. can you continue this pattern?can you continue this pattern?
Matching UpMatching Up
00 00
11 11
22 1010
33 1111
44 100100
55 101101
66 110110
77 111111
88 10001000
99 10011001
1010 10101010
1111 10111011
1212 11001100
1313 11011101
1414 11101110
1515 11111111
1616 1000010000
1717 1000110001
1818 1001010010
1919 1001110011
2020 1010010100
2121 1010110101
2222 1011010110
2323 1011110111
2424 1100011000
2525 1100111001
2626 1101011010
The Power of the Powers The Power of the Powers of 2of 2
1 (decimal) 1 (decimal) ≈≈ 1 (binary) 1 (binary) ≈≈ 2 200
10 (decimal) 10 (decimal) ≈≈ 2 (binary) 2 (binary) ≈≈ 2 211
100 (decimal) 100 (decimal) ≈≈ 4 (binary) 4 (binary) ≈≈ 2 222
1000 (decimal) 1000 (decimal) ≈≈ 8 (binary) 8 (binary) ≈≈ 2 233
Any number can be expressed as a sum Any number can be expressed as a sum of powers of 2of powers of 2 e.g. 13 = 8 + 4 + 1 = 2e.g. 13 = 8 + 4 + 1 = 23 + 3 + 222 + 2 + 220 0 ≈≈ 1101 (bin) 1101 (bin) This is your shortcut!This is your shortcut!
Back to the TimeBack to the Time
It’s now 2:26 and 34 secondsIt’s now 2:26 and 34 seconds How do we represent that?How do we represent that?
2 becomes 102 becomes 10 26 becomes 1101026 becomes 11010 34 becomes 10001034 becomes 100010
The current time is: 10 11010 100010The current time is: 10 11010 100010
Your Task…Your Task…
Write a program in Turing that…Write a program in Turing that… Gets the current time from the systemGets the current time from the system
Look in the command reference for “Time”Look in the command reference for “Time”
Prints it out to the console in binary formatPrints it out to the console in binary format e.g., 2:26:34 prints out as:e.g., 2:26:34 prints out as:
10 10 11010 11010 100010100010
Our next project will involve LED lightsOur next project will involve LED lights