1 / 10

CS 140 Lecture 14

CS 140 Lecture 14. Professor CK Cheng 11/14/02. Part II. Standard Modules. Interconnect Operators. Adders Multiplier Adders 1. Representation of numbers 2. Full Adder 3. Half Adder 4. Carry Look Ahead Adder. 1. Representation. id 0 1 2 3 4 5 6 7 8. Sign magnitude 1000

airell
Download Presentation

CS 140 Lecture 14

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CS 140 Lecture 14 Professor CK Cheng 11/14/02

  2. Part II. Standard Modules • Interconnect • Operators. Adders Multiplier • Adders 1. Representation of numbers • 2. Full Adder • 3. Half Adder • 4. Carry Look Ahead Adder

  3. 1. Representation id 0 1 2 3 4 5 6 7 8 Sign magnitude 1000 1001 1010 1011 1100 1101 1110 1111 2s Compliment 0000 1111 1110 1101 1100 1011 1010 1001 1000 4 bit 0000 0001 0010 0011 0100 0101 0110 0111 1s Compliment 1111 1110 1101 1100 1011 1010 1001 1000

  4. Examples 2 + 3 = 5 0 0 1 0 + 0 0 1 1 0 1 0 1 2 - 3 = -1 (1’s) 0 0 1 0 + 1 1 0 0 1 1 1 0 -2 - 3 = -5 (2’s) 1 1 1 0 + 1 1 0 1 1 0 1 1 -2 - 3 = -5 (1’s) 1 1 1 0 + 1 1 0 0 1 0 0 1 2 - 3 = -1 (2’s) 0 0 1 0 + 1 1 0 1 1 1 1 1 Checking for overflow -3 + -5 = -8 1 1 0 1 + 1 0 1 1 1 0 0 0 1 1 1 1 C5C4 3 + 5 = 8 0 0 1 1 + 0 1 0 1 1 0 0 0 1 1 1 C5C4

  5. b b’ a C4 MUX overflow minus C3 Adder Cout Sum

  6. 2. Full Adder a b cin sum = a + b + cin cout = ab + a cin + b cin = ab + (a + b)cin FA Sum cout a + b = a + b if ab = 0 a + b + ab = a + b + ab c 0 0 0 0 a 0 0 1 1 b

  7. Id a b cin carry sum 0 0 0 0 0 0 1 0 0 1 0 1 2 0 1 0 0 1 3 0 1 1 1 0 4 1 0 0 0 1 5 1 0 1 1 0 6 1 1 0 1 0 7 1 1 1 1 1 Sum = a + b + Cin Cout = ab + aCin + bCin

  8. 3. Half Adder a b Sum = ab’ + a’b = a + b Cout = ab HA Sum cout a b Cout a b Cout sum 0 0 0 0 0 1 0 1 1 0 0 1 1 1 1 0 Sum

  9. x cout carryout HA a OR sum a + b b HA sum cin

  10. 4. Carry Look Ahead Adder C1 = a0b0 + (a0+b0)c0 = q0 + p0c0 C2 = a1b1 + (a1+b1)c1 = q1 + p1c1 = q1 + p1q0 + p1p0c0 C3 = a2b2 + (a2+b2)c2 = q2 + p2c2 = q2 + p2q1 + p2p1q0 + p2p1p0c0 C4 = a3b3 + (a3+b3)c3 = q3 + p3c3 = q3 + p3q2 + p3p2q1 + p3p2p1q0 + p3p2p1p0c0 qi = aibi pi = ai + bi a3 b3 a2 b2 a1 b1 a0 b0 q3 p3 q2 p2 q1 p1 q0 p0 c0 c4 c3 c2 c1

More Related