Essence of Computation CSCI N100 Essence of Computation Learning how computers think

Definition of computer Universal Information Manipulator

Universal Works with all kinds of information Does all kinds of stuff to it Very few limitations

Information Seems to be able to work with anything Actually very limited Tiny pieces of data combined into complex information

Manipulator Seem able to do anything with data Actually very limited Simple commands combined into complex instructions

Computers and Information Information limited to on/off impulses Like a light switch Infinite positions Two outcomes

Working with Multiple Switches One switch - two messages Two switches - four messages Three switches - eight messages

Assigning Values to messages Looking at the pattern 1, 2, 4, 8, 16, 32, 64, 128... Seeing how it works…

Conversion Chart Binary to Decimal 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1  

Conversion Chart Binary to Decimal 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0

Conversion Chart Binary to Decimal 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0  8x1  4x1  0x2  1x0

Conversion Chart Binary to Decimal 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0  8x1  4x1  0x2  1x0  8+  4+  0+ 1101 = 13

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1   22

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1   22 The 1st number that is equal to or less than the decimal number

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1 22 Subtract 22 – 16 remainder of 6

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1 22 Subtract 22 – 16 remainder of 6

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0 Subtract 22 – 16 remainder 6 Subtract 6 – 8?

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0 Subtract 22 – 16 remainder 6 Subtract 6 – 8? Subtract 6 – 4 remainder 2

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0 Subtract 22 – 16 remainder 6 Subtract 6 – 8? Subtract 6 – 4 remainder 2 Subtract 2 – 2 remainder 0

Conversion Chart Decimal to Binary 28 27 26 25 24 23 22 21 20 256 128 64 32 16 8 4 2 1    1  0 22 = 10110