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1 Our focus is on making n-bit circuit using 1-bit building block Comparing two n-bit numbers for their equality – A ----> A n-1 A n-2 …………A 0 – B ---->

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Presentation on theme: "1 Our focus is on making n-bit circuit using 1-bit building block Comparing two n-bit numbers for their equality – A ----> A n-1 A n-2 …………A 0 – B ---->"— Presentation transcript:

1 1 Our focus is on making n-bit circuit using 1-bit building block Comparing two n-bit numbers for their equality – A ----> A n-1 A n-2 …………A 0 – B ----> B n-1 B n-2 ………….B 0 First, we shall compare the two numbers for equality Start with MSB and compare one bit at a time If the bit of one number is greater than the corresponding bit of the other number, then the number is greater. This becomes the solution Else, i.e if the two bits are equal, then compare the next bit. Repeat the last two steps n-bit comparator using 1-bit comparator

2 2 1-bit comparator forms the building block for comparing two n-bit numbers. E is the cascading signal E i+1 is the Cascading input, E i is the cascading output E i+1 = 1 implies that the two numbers are not equal so far E i+1 = 0 implies that the two numbers are equal so far If E i+1 = 1, then E i = 1 Else, E i = E i+1 + (Ai XOR Bi ) Basic building block for n-bit comparator AiBi E i+1 Ei

3 3 Using the building block, we can build an n-bit comparator circuit What is the value of input E n ? The final result is, if E 0 = 0, then A = B and if E 0 = 1, then A != B Using 1-bit building blocks to make n-bit circuit A n-2 B n-2 En E n-1 E1E1 E0E0 A n-1 B n-1 A0A0 B0B0

4 4 Next, we compare the two numbers for A > B, A = B or A < B The basic building block for the purpose is as shown –The primary inputs are Ai and Bi –Cascading inputs are (A>B) in, (A=B) in and (AB) out, (A=B) out and (AB) out = (A>B) in + (A=B) in. (A i.B i ’ ) (AB) in (A=B) in (AB) out (A=B) out (A { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3422226/slides/slide_3.jpg", "name": "4 Next, we compare the two numbers for A > B, A = B or A < B The basic building block for the purpose is as shown –The primary inputs are Ai and Bi –Cascading inputs are (A>B) in, (A=B) in and (AB) out, (A=B) out and (AB) out = (A>B) in + (A=B) in.", "description": "(A i.B i ’ ) (AB) in (A=B) in (AB) out (A=B) out (A

5 5 The 1-bit complex comparator block is modified to have fewer cascading signals It has two primary inputs, two cascading inputs, and two cascading outputs The equations for the outputs are (A>B) out = (A>B) in + (AB) out and (AB) in (AB) out (A { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3422226/slides/slide_4.jpg", "name": "5 The 1-bit complex comparator block is modified to have fewer cascading signals It has two primary inputs, two cascading inputs, and two cascading outputs The equations for the outputs are (A>B) out = (A>B) in + (AB) out and (AB) in (AB) out (A

6 6 The 1-bit maximizer block is similar to the simplified complex comparator It has two primary inputs, one primary output, two cascading inputs, and two cascading outputs The primary output M is 1 if depending on which input is greater The equations for the outputs are –(A>B) out = (A>B) in + (AB)in. A + (AB)in’. (AB) in (AB) out (A { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/12/3422226/slides/slide_5.jpg", "name": "6 The 1-bit maximizer block is similar to the simplified complex comparator It has two primary inputs, one primary output, two cascading inputs, and two cascading outputs The primary output M is 1 if depending on which input is greater The equations for the outputs are –(A>B) out = (A>B) in + (AB)in. A + (AB)in’. (AB) in (AB) out (A


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