Adding numbers

Adding Numbers Friday, 4 October 13

High Level Languages • Java • C# • Haskell Friday,
4 October 13

High Level Languages • c * seriously Friday, 4 October
13

Syntactic Sugar • + operator Friday, 4 October 13

Friday, 4 October 13

Bitwise Operators • ‘AND’ - takes two binary inputs. Returns
1 if both are 1, otherwise 0 0 and 0 -‐-‐> 0 0 and 1 -‐-‐> 0 1 and 0 -‐-‐> 0 1 and 1 -‐-‐> 1 Friday, 4 October 13

Bitwise Operators • ‘XOR’ - Exclusive OR. Returns 1 if
one or the other inputs is 1, but not neither and not both. 0 xor 0 -‐-‐> 0 0 xor 1 -‐-‐> 1 1 xor 0 -‐-‐> 1 1 xor 1 -‐-‐> 0 Friday, 4 October 13

Bit Shifting • Left-shift - moves all the 1’s across
to the left 0001 0110 (22) -‐> 0010 1100 (44) • Right-shift - moves all the 1’s across to the right 0001 0110 (22) -‐> 0000 1011 (11) Friday, 4 October 13

The Formula • Start with two numbers: x and y
set a = (x AND y) set b = (x XOR y) set x = a left-shifted by 1 set y = b -- keep going until a is 0. The answer is b Friday, 4 October 13

E.G. 10 + 7 1010 & 0111 -‐-‐-‐-‐
0010 -‐> Left-‐shifted -‐> 0100 (4) 1010 ^ 0111 -‐-‐-‐-‐ 1101 (13) Friday, 4 October 13

E.G. 4 + 13 0100 & 1101 -‐-‐-‐-‐

E.G. 8 + 9 1000 & 1001 -‐-‐-‐-‐

E.G. 16 + 1 10000 & 00001 -‐-‐-‐-‐

Adding Numbers in C int add(int x, int y) {
int a,b; do { a = x & y; b = x ^ y; x = a << 1; y = b; } while (a); return b; } Friday, 4 October 13

recursion! int add(int x, int y) { int a,b;
if (x == 0) return y; a = (x & y) << 1; b = x ^ y; return add(a, b); } Friday, 4 October 13

recursion! int add(int x, int y) { if (x
== 0) return y; return add((x & y) << 1, x ^ y); } Friday, 4 October 13

just for fun... import Data.Bits add :: (Bits a) =>
a -‐> a -‐> a add a b | a == 0 = b | otherwise = add ((a .&. b) `shiftL` 1) (a `xor` b) https://gist.github.com/IanRandall/6775842 Friday, 4 October 13

Adding numbers

Adding numbers

Ian Randall

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Adding Numbers Friday, 4 October 13

High Level Languages • Java • C# • Haskell Friday,

High Level Languages • c * seriously Friday, 4 October

Syntactic Sugar • + operator Friday, 4 October 13

Friday, 4 October 13

Bitwise Operators • ‘AND’ - takes two binary inputs. Returns

Bitwise Operators • ‘XOR’ - Exclusive OR. Returns 1 if

Bit Shifting • Left-shift - moves all the 1’s across

The Formula • Start with two numbers: x and y

E.G. 10 + 7 1010 & 0111 -‐-‐-‐-‐

E.G. 4 + 13 0100 & 1101 -‐-‐-‐-‐

E.G. 8 + 9 1000 & 1001 -‐-‐-‐-‐

E.G. 16 + 1 10000 & 00001 -‐-‐-‐-‐

Adding Numbers in C int add(int x, int y) {

recursion! int add(int x, int y) { int a,b;

recursion! int add(int x, int y) { if (x

just for fun... import Data.Bits add :: (Bits a) =>