3.8: Logical Operators

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Most programmers have seen logical operators in HLL for Boolean data types. As was covered earlier in this text, there are often two form of these operators, the logical (or short-circuiting) operators and the bitwise operators. MIPS only implements the bitwise operators, but they are called logical operators. Since all Boolean operations can be implemented with only 3 operations, the AND, OR, and NOT operations, this sections will present these 3 operations. In addition the XOR operation will be included for convenience because it is often easier to state a logical expression using XOR than to do so using AND, OR, and NOT. See the problems at the end of the chapter to see how to implement logical operations using these 4 basic logic operations.

The logic operators covered are:

and operator, which has three formats. The first format is the only real format of this operator. The operator does a bit-wise AND of R_s and R_t and stores the result R_d register. The format and meaning of this operator is:

format:	`and R_d, R_s, R_t`
meaning:	`R_d <- R_s AND R_t`

The second format of the and operator is a pseudo instruction. In this case the 3rd operator is immediate value, and so this is just a short hand for implementing the andi operator. The format, meaning, and translation of the pseudo operators is as follows:

format:	`and R_t, R_s, Immediate`
meaning:	`R_t <- R_s AND Immediate`
translation:	`andi R_t, R_s, Immediate`

The third format of the and operator is also a pseudo instruction, and strange in that only logical operators have this format. In this instruction, R_s and R_t are assumed to be the same register, and the 3rd operator is immediate value The format, meaning, and translation of the pseudo operators is as follows:

format:	`and R_s, Immediate`
meaning:	`R_s <- R_s AND Immediate`
translation:	`andi R_s, R_s, Immediate`

andi operator. The operator does a bit-wise AND of R_s and an immediate value, and stores the result Rt register. The format and meaning of this operator is:

format:	`andi R_t, R_s, Immediate`
meaning:	`R_t <- R_s AND Immediate`

The shorthand with a single register also applies to the andi instruction.

format:	`andi R_s, Immediate`
meaning:	`R_s <- R_s AND Immediate`
translation:	`andi R_s, R_s, Immediate`

or operator, which has three formats. The first format is the only real format of this operator. The operator does a bit-wise OR of R_s and R_t and stores the result R_d register. The format and meaning of this operator is:

format:	`or R_d, R_s, R_t`
meaning:	`R_d <- R_s OR R_t`

The second format of the and operator is a pseudo instruction. In this case the 3rd operator is immediate value, and so this is just a short hand for implementing the ori operator. The format, meaning, and translation of the pseudo operators is as follows:

format:	`or R_t, R_s, Immediate`
meaning:	`R_t <- R_s OR Immediate`
translation:	`ori R_t, R_s, Immediate`

The shorthand with a single register also applies to the or instruction.

format:	`or R_s, Immediate`
meaning:	`R_s <- R_s OR Immediate`
translation:	`andi R_s, R_s, Immediate`

ori operator. The operator does a bit-wise OR of R_s and an immediate value, and stores the result R_t register. The format and meaning of this operator is:

format:	`ori R_t, R_s, Immediate`
meaning:	`R_t <- R_s OR Immediate`

The shorthand with a single register also applies to the ori instruction.

format:	`ori R_s, Immediate`
meaning:	`R_s <- R_s OR Immediate`
translation:	`ori R_s, R_s, Immediate`

xor operator, which has three formats. The first format is the only real format of this operator. The operator does a bit-wise OR of R_s and R_t and stores the result R_d register. The format and meaning of this operator is:

format:	`xor R_d, R_s, R_t`
meaning:	`R_d <- R_s XOR R_t`

The second format of the and operator is a pseudo instruction. In this case the 3rd operator is immediate value, and so this is just a short hand for implementing the ori operator. The format, meaning, and translation of the pseudo operators is as follows:

format:	`xor R_t, R_s, Immediate`
meaning:	`R_t <- R_s XOR Immediate`
translation:	`xori R_t, R_s, Immediate`

The shorthand with a single register also applies to the or instruction.

format:	`xor R_s, Immediate`
meaning:	`R_s <- R_s AND Immediate`
translation:	`xori R_s, R_s, Immediate`

ori operator. The operator does a bit-wise OR of R_s and an immediate value, and stores the result Rt register. The format and meaning of this operator is:

format:	`xori R_t, R_s, Immediate`
meaning:	`R_t <- R_s XOR Immediate`

The shorthand with a single register also applies to the xori instruction.

format:	`xori R_s, Immediate`
meaning:	`R_s <- R_s XOR Immediate`
translation:	`xori R_s, R_s, Immediate`

not operator. The operator does a bit-wise NOT (bit inversion) of R_s, and stores the result R_t register. The format and meaning of this operator is:

format:	`not R_s, R_t`
meaning:	`R_s <- NOT(R_t)`
translation:	`nor R_s, R_t, $zero`

In addition to the real operators, there are a number of pseudo sub operators, which use 32-bit immediate values. The 32-bit values are handled exactly as with the add instructions, with a sign extension out to 32 bits.

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