Bit Shifting

• Manipulation of bits to produce the results desired (e.g., addition, subtraction, multiplication, etc)

AND

• & operator
• The and operation shows what are the carries (vai um)
• The in order for the carries to be properly added, they need to be shifted to the left

let a = 6; // 0000 0110
let b = 12; // 000 01100

println!("{:08b}", a & b); // 0000 0100 (4)

OR

• | operator

let a = 6; // 0000 0110
let b = 12; // 000 01100

println!("{:08b}", a | b); // 0000 1110 (14)

XOR

• ^ operator
• The xor operator "simulates" a sum by showing what are the sum of the elements ignoring the carries

let a = 6; // 0000 0110
let b = 12; // 000 01100

println!("{:08b}", a ^ b); // 0000 1010 (10)

NOT

• ~ operator

let a = 6; // 0000 0110

println!("{:08b}", a ~ b);

Shift Left

• << operator
• Multiplies by 2

let a = 6; // 0000 0110

println!("{:08b}", a << 1); // 0000 1100 (12)

Shift Right

• >> operator
• Divides by 2

let a = 6; // 0000 0110

println!("{:08b}", a >> 1); // 0000 0011 (3)

Carry

• Generate a carry: no carry is receiving, but a carry is created
• Propagate a carry: a carry is received and a carry is created

Applications of bitwise

• Sum
  1. Find the carries &
  2. Shift the carries to the left <<
  3. Add the numbers without the carries ^
  4. Add the sum (without carries) + the left shifted carries &

carry_lookahead = ((a & b) << 1)

full_adder = (a ^ b) + carry_lookahead