1 Arithmetic and Logical Operations - Part I

Boolean Operations A boolean variable can only have one of the two values, i.e, can either be 1 or 0. Given a sequence of bits, each of these bits can be considered one boolean variable. A boolean operation is applied simultaneously to each bit. Logical operations are defined for boolean variables.

Unary boolean operations input zero one invert same MAL provides the not operator

Logical Operations aband ornandnorxor xnor Some MAL instructions notD,S 1 andD,S 1,S 2 norD,S 1,S 2

Masking and Merging Masking is the process of extracting a portion of the variables from a cell. A mask can be used to extract the appropriate bits needed for future operations. The and instruction can used to extract bits. Merging is simply inserting a bit sequence in the appropriate part of the cell. The or instruction can be used to merge.

Example 14.1 The following can be used as masks: mask1:.word0xff mask2:.word0x007fffff and mask Extracted bits

Example 14.2 What is the result of using mask1 with the given bit sequence? and

Example and or merged cleared

Example 14.4 Here’s a SAL code that demonstrates masking and merging: mask1:.word0xff smallc:.word0x charc:.word0x not mask, mask1 and charc, mask, charc #clear bits or charc, charc, smallc #merge

Shift Operations Sometimes it is necessary to move a sequence of bits to different positions within the word, e.g. we need to align variables before merging A shift operation rearranges the bits within the cell by shifting them There are three types of shift operation: logical, rotate and arithmetic.

Logical Shift A logical shift moves the bits within the cell one position to the right or to the left In a logical right shift, the least significant bit (lsb) is discarded and the most significant bit (msb) is assigned 0. In a logical left shift, the lsb is assigned 0 and the msb is discarded. A shift instruction will have an operand that specifies how many times the one position shift is applied.

Example in discard MAL instruction: srl D,S 1,AMT y x

Example SAL instruction: sll D,S 1,AMT 0 in discard y x

Rotate A rotate operation shifts the bits within the cell without discarding. Unlike the logical shift, no information is lost in a rotate operation. A rotate operation can either be left or right. A rotate left has an equivalent rotate right operation. A rotate right places the lsb into the msb position. A rotate left places the msb into the lsb position.

Example 14.7 SAL instruction: rol x,y, y x

Example y What is the result of SAL’s ror x,y,2 ?

Arithmetic Shift A right shift is equivalent to integer division by two. A left shift is equivalent to multiplication by two. In 2’s complement, positive or negative, a logical left shift, is equivalent to multiplication by two. An arithmetic left shift is the same as a logical left shift.

An arithmetic right shift replicates the sign bit, instead of filling in with 0’s as in the logical right shift. In 2’s complement, positive or negative, division by two is accomplished via an arithmetic right shift. There is no arithmetic left shift instruction because the logical left shift instruction produces identical result.

Example replicated y x discard SAL instruction: srax,y,1

20 Example What is the result of multiplying this by two?