15 213 Intro to Computer Systems Recitation 1 By sseshadr Today Introductions Datalab Tricks Floating point questions Go to Office Hours Integer Puzzles Parity Example Style Introductions Datalab Tricks Basics vs vs vs What is x int x 9 12 1 x 26 Datalab Tricks Trick 1 Signed ness The MOST significant bit 0 positive or zero 1 negative What is int x 10 31 int y 10 31 It s NOT 1 what is arithmetic shifting How do we fix that Answers x 0 and y 1 Datalab Tricks Trick 2 Properties of Zero Masking 0 something 0 why 0 1 something something why Why is this useful Positive zero vs negative zero int x 0 int y x Neither x nor y is negative MSB is 0 for both Why is this useful Datalab Tricks Trick 3 Negation Review take a 5 bit twos compliment system 1 0 0 1 0 24 23 22 16 2 14 21 20 Datalab Tricks Trick 3 Negation Review take a 5 bit twos compliment system 0 1 1 1 0 24 23 22 8 4 2 14 21 20 Datalab Tricks Trick 3 Negation Example 1 0 0 1 0 0 1 1 0 1 0 1 1 1 0 int x 14 14 int y x 13 int z x 1 14 Datalab Tricks Trick 3 Negation In general x x 1 Does this always work Tmin No Tmax Yes Zero Yes Everything else Yes Integer Puzzles Integer Puzzles x 0 x 2 0 Nope Tmin ux 0 Yup x 7 7 x 30 0 Yup x 7 7 means last 3 bits are 1 Examine the negative bit of x 30 Integer Puzzles ux 1 Nope Unsigned comparison means 1 is Umax x y x y Nope Boundary cases x 0 y Tmin what is Tmin x x 0 Nope Overflow into negative bit int x 65535 2 16 1 Integer Puzzles x 0 y 0 x y 0 Nope Overflow into negative bit x y Tmax x 0 x 0 Yup Why doesn t break for Tmax x 0 x 0 Nope What is Tmin Integer Puzzles x x 31 1 Nope x 0 ux 3 ux 8 Yup x 3 x 8 Nope Careful on rounding int x 19 int y x 3 y 3 int z x 8 z 2 Integer Puzzles x x 1 0 Nope x 0 x 1 Parity Example Write a function which takes an integer and returns 1 if there are an odd number of 1 bits 0 if there are an even number of 1 bits int parity check int x Any ideas Parity Example Inspiration If we could XOR all of the bits in the argument we would get the answer 11011001011000111110010100101101 11011001011000111110010100101101 XOR 1101100101100011 1110010100101101 0011110001001110 down to 16 bits Parity Example Just keep going 0011110001001110 0011110001001110 XOR 00111100 01001110 01110010 down to 8 bits Parity Example Just keep going 01110010 01110010 XOR 0111 0010 0101 down to 4 bits Parity Example You can take it from there Still confused on high level algorithm Can t write the C code for the Parity Problem Office Hours Style Here is what we grade on http www cs cmu edu 213 codeStyle html It is in your best interest to read it ASAP Autolab isn t the whole grade We read your code Style Documentation Whitespace Line length Variable names Magic Numbers Dead Code Modularity Error checking Consistency
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