Arithmetic Circuits II

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Arithmetic Circuits II
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Multiplier

• Given the multiplicand, B B1 B0
• and the multiplier
• A A1 A0
• Then we multiply by doing single-bit
  multiplications and shifts

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Combinational Multiplier
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Multiplication of Larger Numbers

• Example
• 4-Bit Multiplicand
• B B3 B2 B1 B0
• 3-Bit
• Multiplier A A2 A1 A0
• Product is a 7-Bit number,
• C C6 C5 C4 C3 C2 C1 C0

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Computing the Product

• Let us work out the multiplication on the board

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Larger Multiplier
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Sign Extension

• Changing the number of bits used to store a
  number is common
• Example
• -5 in stored in 4-bits (1011)
• to store -5 in 8 bits, extend the Sign Bit in
  the 4 left most bits
• 1011 is changed to 1111 1011
• 1011 -5
• 1111 1011 is also -5

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Weve Covered

• Adders
• Ripple carry
• Carry lookahead
• Subtracting unsigned numbers
• New design for adder-subtractor
• Signed numbers
• Signed addition/subtraction
• Multiplication just basic
• Modified Circuits