Operations on bits (bitwise operations)

Example:

int pixel {102345}; // stores some pixel color value

to make darker by a factor of 2, we just need to halve each byte component - would need to use bitwise operations

Example: to change the way devices work, we may want to flip bits in a register

srl, sll - shift right logical and shift left logical

Example (srl, sll):

srl $t1, $t0, 2 # shift 2 bits right
sll $s0, $s5, 3 # shift 3 bits left

• bits that "fall off" are discarded
• "empty" bits as a result are filled with zeroes

Example (c++):

int a,b;
b = a << 2;
b = a >> 1;

Example (shifting one position left):

0000 0011 = 3
0000 0110 = 6
0000 1100 = 12
0001 1000 = 24

each shift multiplies by 2

Example (shifting one position right):

1100 = 12
0110 = 6
0011 = 3
0001 = 1

each shift does int division by 2

Note: srl and sll are preferred to mult or div when using powers of 2, because they are much more simple (and efficient)

Other binary operations:

"pipe" above is | (markdown table formatting makes it hard to write)

Example:

and $t4, $t3, $t1 # t4 = t3 & t1
andi $t4, $t3, 6 # t4 = t3 & 6

also, xori and ori operators exist.

Other things to do with bit operations:

• flip a specific bit
• set a specific bit
• clear a specific bit
• get a specific bit

When counting bits, we go right to left, counting from 0 to 31. (again, in this course we assume 32-bit word size.)

So for example, bit #2 of a number is the 4s place (in general, bit X is the 2^X place)

Example:

# s0 holds value. goto L1 if bit #2 is set.

addi $t0, $zero, 4 # create mask
and $t1, $s0, $t0 # apply mask to s0
bne $t1, $zero, L1 # goto L1 if bit was set

in this case the and will zero out the value if bit #2 was not set and give the result of the mask if it is set, so the bne will only jump if the bit was set.

(note: in above code, the addi and and could have been collapsed into a single andi instruction, but was separated for pedagogical purposes.)

Example: set bits 4 and 6 in s0

# create mask - 01010000
addi $t0, $zero, 0x50 # create mask
or $s0, $s0, $t0 # apply mask

note - in above code, could have used ori operator as well.

note - in the above code, we use 0x50 because this is the shorter hex version of 01010000. it is easy to convert - split into groups of 4 binary digits and convert each to hex. for example, 0101 is 5 and 0000 is 0, so we get 0x50.