Ch04a-Arithmetic

Ch04a-Arithmetic - Clark Guest 2009 ECE 25 Logic and...

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Arithmetic Functions ECE 25 Chapter 4 ©Clark Guest 2009 ECE 25 Logic and Computer Design Topics Binary Addition Negative Binary Numbers Overfow Other Arithmetic Hardware Description Languages 2 ©Clark Guest 2009 ECE 25 Logic and Computer Design Binary Hal± Adder (No Carry Input) A B C S 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 C = A • B S = A ! B A B S C ©Clark Guest 2009 ECE 25 Logic and Computer Design Binary Addition Carry 1 1 1 1 A 0 0 1 1 0 1 0 1 B 0 0 0 1 1 1 0 0 Sum 0 1 0 1 0 0 0 1 (n) (n+1) A n B n C n S n C n+1 0 0 0 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 0 0 1 0 1 0 1 0 1 1 1 0 0 1 1 1 1 1 1 A\BC 00 01 11 10 0 1 0 1 0 1 1 0 1 0 A\BC 00 01 11 10 0 1 0 0 1 0 0 1 1 1 S n C n+1 A ! B ! C AB+AC+BC =AB+(A+B)C =AB+(A ! B)C+ABC =AB(1+C)+(A ! B)C =AB+(A ! B)C A B C n+1 C n S n Full Adder
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©Clark Guest 2009 ECE 25 Logic and Computer Design Multi-Bit Addition Full Adder B 0 A 0 S 0 C 0 Full Adder B 1 A 1 S 1 C 1 Full Adder B 2 A 2 S 2 C 2 Full Adder B N A N S N C N C 3 Overfow • • • ©Clark Guest 2009 ECE 25 Logic and Computer Design Negative Binary Numbers Decimal Sign Magnitude Two’s Complement 4 0100 0100 3 0011 0011 2 0010 0010 1 0001 0001 0 0000 0000 -1 1001 1111 -2 1010 1110 -3 1011
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Ch04a-Arithmetic - Clark Guest 2009 ECE 25 Logic and...

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