1. Ch. 7 Bitwise Operations
Comp Sci Bitwise operations

2. Comp Sci 251 -- Bitwise operations
Shift and rotate
Move bits around within a register
Fast implementation of certain arithmetic
Logical operations (and, or, xor, nor, not)
Combine two bit patterns
Affect selected bits in a word
Comp Sci Bitwise operations

3. Shift left instructions
Bits move left
Rightmost bits are cleared
sll Rdest, Rsrc1, immediate
sllv Rdest, Rsrc1, Rsrc2
Bits from Rsrc1 shifted left by immediate or Rsrc2
Result  Rdest (Rsrc1 unchanged)
Sslv ssl variable 1 1 1 1 1
Comp Sci Bitwise operations

4. Shift left and multiplication
sll $t0, $t0, 1 # multiply by 2
sll $t0, $t0, 2 # multiply by 4
sll $t0, $t0, 3 # multiply by 8
Shift left n multiplies by 2n
Comp Sci Bitwise operations

5. Practical use of shift left
int x[50];
x[3] = -1;
.text
li $t0, -1
li $t1, 3
sll $t1, $t1, 2
sw $t0, x($t1)
.data
.align 2
x:.space 200
Comp Sci Bitwise operations

6. Shift right instructions
Bits move right
Leftmost bits
Cleared (logical shift)
Retain original leftmost bit value (arithmetic shift)
srl Rdest, Rsrc1, immediate
srlv Rdest, Rsrc1, Rsrc2
sra Rdest, Rsrc1, immediate
srav Rdest, Rsrc1, Rsrc2
Logical shift right 1 1 1 1 1
Arithmetic shift right 1 1 1 1 1
Comp Sci Bitwise operations

7. Shift right and division
srl $t0, $t0, 1 # divide by 2
srl $t0, $t0, 2 # divide by 4
Shift right logical n divides by 2n (unsigned)
Shift right arithmetic n divides by 2n (signed)
Comp Sci Bitwise operations

8. Comp Sci 251 -- Bitwise operations
Rotate instructions
Similar to shift
Bits pushed out wrap around
rol Rdest, Rsrc1, Src2
ror Rdest, Rsrc1, Src2
Bits from Rsrc1 rotated by Src2
Result  Rdest (Rsrc1 unchanged)
Rotate left 1 1 1 1 1
Comp Sci Bitwise operations

9. Comp Sci 251 -- Bitwise operations
Logical instructions x y
x and y
x or y
x xor y
x nor y
not x 1
Comp Sci Bitwise operations

10. Comp Sci 251 -- Bitwise operations
Logical instructions
and Rdest, Rsrc1, Src2
or Rdest, Rsrc1, Src2
xor Rdest, Rsrc1, Src2
nor Rdest, Rsrc1, Src2
not Rdest, Rsrc
Corresponding bits of Rsrc1 and Src2 are combined w/ logical operator
Resulting word  Rdest
Comp Sci Bitwise operations

11. Comp Sci 251 -- Bitwise operations
Logical Instructions
Name Format Operation
And R and Rdest, Rsrc1, Src2
R[rd] = R[rs] & R[rt]
And immediate I
andi R[rt] = R[rs] & ZeroExtImm
Comp Sci Bitwise operations

12. Uses of shift/logical instructions
Clear: AND with 0
Set: OR with 1
Toggle: XOR with 1
Applications:
Hashing
Data compression
Checksums
Graphics
Exercises:
Clear low order 4 bits of $t0
Set the most significant bit of $t1
Count number of "1" bits in $t2
Comp Sci Bitwise operations

13. Examples in /shared/huen/251/ch07_bitwise
bit2.a – extracts three fields of different widths from a 32 bit word
xor.a – XOR operation. Use XSPIM or PCSPIM to see how the bit pattern changes in registers.
xori.a – another XOR operation example.
Comp Sci Bitwise operations

14. Examples in /shared/huen/251/ch07_shift
dec.a - asks user for decimal number, converts to ASCII string, print the result.
hex.a – asks user for decimal number, converts to hexadecimal, print the result
logic1.a – sums the elements that are NOOT multiples of 4 in an array.
Oct.a - asks user for decimal number, converts to octal, print the result
Comp Sci Bitwise operations