08_Arithmetic_background

08_Arithmetic_background - Design Design of Arithmetic...

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esign of Arithmetic Units Design of Arithmetic Units ECE152B AU 1
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esign of Arithmetic Units Design of Arithmetic Units ill di th d i f We will discuss the design of Adders/Substractors Multipliers/Dividers and analyze algorithms & methods to perform d i d ti ithi tb l the desired operations within an acceptable time. ddition Addition A basic cell is the full adder (FA) ECE152B AU 2
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A i B i C in B C C out =A i B i +B i C in +A i C in F =A B C A in Cot F FA i i i in C out F I AI-H BI-H BI-H AI-H COUT-H CIN-H CIN-H FI-H ECE152B AU 3 AI-H
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word adder composed of full adders: A word adder composed of full adders: A 7 B 7 A 6 B 6 A 5 B 5 A 4 B 4 A 3 B 3 A 2 B 2 A 1 B 1 A 0 B 0 A B C in FA A B C in FA A B C in FA A B C in FA A B C in FA A B C in FA A B C in FA A B C in FA Cot F Cot F Cot F Cot F Cot F Cot F Cot F Cot F C out F 7 F 6 F 5 F 4 F 2 F 1 F 0 F 3 ECE152B AU 4
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This kind of addition process is called a ripple carry adder , since the carry at each stage is propagated to the next stage. For an N-bit addition: (G: one gate delay) T ADD RCA =N × T FA = N × (2 × G) Ripple carry adders are an example of a minimal gate solution, but the time required for the result may not be acceptable. Look-ahead carry adder (LACA): more hardware while faster ECE152B AU 5
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ow look at the logic equation of Cout: Now look at the logic equation of Cout: C out = AB+AC in +BC in = AB+C in (A+B) If AB is asserted, there will be a carry gardless of the value of the carry input: this regardless of the value of the carry input: this term (AB) is called the carry generate (CG) nction. function. If (A+B) is asserted, any carry supplied to his stage is passed on to the next: this term t s stage s passed o to t e ext: t s te (A+B) is called the carry propagate (CP) function. ECE152B AU 6
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Data In Carry in LACA AB C i n CG CP Carry Generate Carry Propagate F Sum out The time required to create the carry generate and carry propagate is a single gate delay.
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08_Arithmetic_background - Design Design of Arithmetic...

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