Topic 11: Arithmetic Circuits Adders and Multipliers

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Topic 11Arithmetic Circuits Adders and
Multipliers

• SFSU ENGR 852
• Spring 2003
• 4/19

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Datapaths

• Manipulate data
• Arithmetic
• Add, multiply
• Format
• UART 8 bits ? 10 bits
• Serial to parallel
• Translate
• BCD to binary

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Ripple Adder
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Full adder
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Full Adder
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Half Adder
Half
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Ripple Adder
H
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What to do?
How do you make this faster?
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Carry-skip (Or carry-bypass)
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Carry-skip (Or carry-bypass)
P4 G4 P5 G5 P6 G6
P7 G7
BPP4P5P6P7
C0,7
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Carry Select
A0 B0 A1 B1 A2 B2
A3 B3
C03
A4 B4 A5 B5 A6 B6
A7 B7
0
C07
A4 B4 A5 B5 A6 B6
A7 B7
S74
1
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Other Addition Speed-up Methods

• Lookahead
• Logarithmic carry lookahead
• Lookahead trees
• Tree adders
• Radix-2 Kogge-Stone tree adder
• Brent-Kung tree adder
• Transistor level speed up methods
• Manchester carry chain
• Domino adders
• Ling Adders

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Other Fast Multipliers

• Wallace Tree Multiplier
• Pipelining
• Booth Encoding

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Booth Encoding

• Rules
• If was 0 and is 0 then add 0
• If was 0 and is 1 then subtract multiplicand
• If was 1 and is 1 then add 0
• If was 1 and is 0 the add multiplicand

0111101 x 0110010
0000000 -0111101 0111101
0000000 -0111101
0000000 0111101 0000000
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Booth Encoding Example
1100 x 0110
0000 -1100 0000
1100 100100 7210
12 x 6 72