__Arithmetic and Logic Operations__

__Intro__

__All arithmetic operation in MIPS uses R-Type instruction format where all 3 operands are registers which consists of the destination (rd), source (rs) and target (rt). In arithmetic and logic operations, small constants are used frequently and made up 50% of operands. For example, ' a = a +5 ' or ' a > 5'.__

There are 3 ways of specifying constant in MIPS:

- Store in memory and load them.
- Using register $0 that load constant zero.
- Using immediate values.

__Logic Operation__

1. Addition

As stated it uses the the R-type instruction format which consists of the opcode and the operands. It has several opcodes such as :

(a) add = addition (R-Type)

(b) addi = add immediate (I-Type)

(c) addiu = add immediate unsigned number (I-Type)

(d) addu = add unsigned number (R-Type)

For addi and addiu, it doesn't use the R-Type format but instead uses the I-Type format where we use a constant replacing the target(rt) register in R-Type.

Extra Note:

- Signed arithmetic are real numbers where (+)ve and (-)ve counts represented in a 32-bit 2's complement binary digit. They may generate an overflow.
- Unsigned arithmetic are numbers that are always (+)ve and will
**never**generate an overflow.

2. Subtraction

Just like addition we also uses the R-Type and the I-type format in subtraction. Examples of instructions are :

(a) sub = subtraction (R-Type)

(b) subi = sub immediate (I-Type)

(c) subu = sub unsigned (R-Type)

3. Multiplication & Division

For Multiplication and division logic operation, the results obtained may be larger than 32-bits. Thus, we use 2 special 32-bits registers designed specifically for multiplication and division operations. These are called (hi = holds the upper 32-bits number) and (lo = holds the lower 32-bits number).

Example of MIPS instruction are:

(a) mult, $s1, $s2 (multiply register s1 and s2)

(b) div, $t1, $t2 (divide register t1 by t2)

To use the hi and lo we uses the instruction code " mflo " or " mfhi ". Examples are:

(a) mult, $s1, $s2 # This is the operation

mfhi $s3 # Moves the upper 32-bits number of the product into register s3

mflo $s4 # Moves the lower 32-bits number of the product into register s4

This is the same for division except for " lo " in division it gets the quotient and for " hi " in divison it gets the remainder.

(b) div, $t1, $t2 # This is the operation

mflo $t3 # Puts the quotient of the product into register t3

mfhi $t4 # Puts the remainder of the product into register t4

4. Shift operation

There are 3 basic shift operations which are:

(a) sll (

**S**hift**L**eft**L**ogical = shifts the 32-bits number to the left and fill up the empty spaces with 0's )
Example:

Shift left by 4-bits

**1001**0001 1011 1100 0000 1010 0000 1111

becomes

0001 1011 1100 0000 1010 0000 1111

**0000*******The 4-bits number (1001) vanish as we shifted to the left by 4-bits and we add four 0's the fill up the

empty space left in the 32-bits number.

(b) srl (

**S**hift**R**ight**L**ogical = shifts the 32-bits number to the right and fill up the empty spaces with 0's)
Example:

Shift right by 4-bits

1111 0000 1010 1001 1001 1010 0000

**1111**
becomes

**0000**1111 0000 1010 1001 1001 1010 0000

*****This time the 4-bits to the right(1111) vanished as we shifted the number to the right. The empty

space is fill with 0's as usual.

(c) sra (

**S**hift**R**ight**A**rithmetic = shifts right nad fills empty space with sign extending)
Example:

Shift right arithmetic by 4-bits (sign +)

1010 0101 1001 1111 1010 0101 0110

**1010**
becomes

**0000**1010 0101 1001 1111 1010 0101 0110

* The sign (+) extend means the empty spaces is filled with 0's.

Example:

Shift right arithmetic by 4-bits (sign -)

1010 0101 1001 1111 1000 0101 0110

**0000**
becomes

**1111**1010 0101 1001 1111 1000 0101 0110

* The sign(-) extend means the empty spaces is filled with 1's.

5. logical operation

There are 2 types of basic MIPS shift instruction:

(a) AND = outputs is 1 if and only if both inputs are 1.

(b) OR = outputs is 1 if at least one of the inputs is 1.

(a) AND

For AND logical operators we can assume that the 2 numbers in each register multiply each other to get

the product. Example:

and, $s0, $s1, $s2 # Multiply register s1 and s2 and put the results in in s0.

Let $s1 = 0000 0000 0000 0000 1111 1111 1111 1111

Let $s2 = 1111 1111 1111 1111 0000 0000 0000 1000

Thus, the result in $s0 will be = 0000 0000 0000 0000 0000 0000 0000 1000

Extra Note:

- AND logical operators also uses the R-Type and the I-Type instruction format such as:

(2) andi (I-Type)

(b) OR

For OR logical operators we can assume that the 2 numbers in each register add each other to get the

product. Example:

or, $t0, $t1, $t2 # Add register t1 and t2 and put the result in t0

Let t1 = 0000 0000 0000 0000 0000 0000 0000 1010

Let t2 = 1111 1010 0110 1111 0001 0000 1100 1010

Thus, the result in $t0 will be = 1111 1010 0110 1111 0001 0000 1101 0100

Extra Note:

- OR logical operators uses the R-Type and I-type instruction formats just like AND.

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