Arithmetic and Logical Operations - Part I

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Arithmetic and Logical Operations - Part I
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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.

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Unary boolean operations

• Unary boolean operations
• input zero one invert same
• 0 0 1 1 0
• 1 0 1 0 1
• MAL provides the not operator

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Logical Operations

• a b and or nand nor xor xnor
• 0 0 0 0 1 1 0 1
• 0 1 0 1 1 0 1 0
• 1 0 0 1 1 0 1 0
• 1 1 1 1 0 0 0 1
• Some MAL instructions
• not D,S1
• and D,S1,S2
• nor D,S1,S2

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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.

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Example 14.1

• The following can be used as masks
• mask1 .word 0xff000000
• mask2 .word 0x007fffff
• 01000001100000000000000000110101
• and 00000000011111111111111111111111
• 00000000000000000000000000110101

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Example 14.2

• What is the result of using mask1 with the given
  bit sequence?
• 01000001100000000000000000110101
• and 11111111000000000000000000000000

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Example 14.3

• 01000001100000000000000000110101
• and 00000000011111111111111111111111
• 00000000000000000000000000110101
• 00000000000000000000000000110101
• or 01000011100000000000000000000000
• 01000011100000000000000000110101

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Example 14.4

• Heres a SAL code that demonstrates masking and
  merging
• mask1 .word 0xff000000
• smallc .word 0x63000000
• charc .word 0x43000000
• . . .
• not mask, mask1
• and charc, mask, charc clear bits
• or charc, charc, smallc merge

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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.

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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.

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Example 14.5
y
x
MAL instruction srl D,S1,AMT
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Example 14.6
y
discard
x
SAL instruction sll D,S1,AMT
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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.

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Example 14.7
y
x
SAL instruction rol x,y,1
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Example 14.8
y
What is the result of SALs ror x,y,2 ?
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Arithmetic Shift

• A right shift is equivalent to integer division
  by two.
• A left shift is equivalent to multiplication by
  two.
• In 2s 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.

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• An arithmetic right shift replicates the sign
  bit, instead of filling in with 0s as in the
  logical right shift.
• In 2s 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.

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Example 14.9
y
x
SAL instruction sra x,y,1
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Example 14.10
What is the result of multiplying this by two?