1. CS 140 Lecture 11 Professor CK Cheng 5/09/02

2. Part III - Standard Modules Decoder, Encoder, Mux, DeMux, Shifter, Adder, Multiplexer Interconnect: Decoder, Encoder, Mux, DeMux Operation: Addition, Multiplication, Shift P1 P2 Memory Mux Demux Decoder

3. 1. Decoder 0 y0y1y7y0y1y7 I0I0 I1I1 I2I2 1 2 0123456701234567 En n inputs 2 n outputs If En = 1 Then y i = 1 if (I 2, I 1, I 0 ) = i y = 0 otherwise Description:....

4. Logic Diagram y0y0 I2’I2’ I1’I1’ I0’I0’ y1y1 I2I2 I1’I1’ I0’I0’ En y7y7 I2I2 I1I1 I0I0....

5. Application: Decoder and OR are a universal set. Implement: f 1 (a,b,c) =  m (1,2,3) f 2 (a,b,c) =  m (2,3,5) f 3 (a,b,c) =  m (0,5,6,7) with a 3 –input decoder and OR gates. I0I0 y0y1..y7y0y1..y7 c b a I1I1 I2I2 0123456701234567 Eny1y1 y2y2 y3y3 f1f1 y2y2 y3y3 y5y5 f2f2 y0y0 y6y6 y7y7 f3f3 y5y5

6. Tree of decoders Implement a 4-2 4 decoder with 3-2 3 decoders. I0I0 y0y1y7y0y1y7 I1I1 I2I2 0123456701234567 I0I0 y 8 y 9 y 15 I1I1 I2I2 0123456701234567 d a b c

7. Implement a 6-2 6 decoder with 3-2 3 decoders. En a,b,c d,e,f y0y0 y7y7 y8y8 y 15 d,e,f y 56 y 63

8. 1. Encoder y n-1 En A I 2 n -1 8 inputs 3 outputs y0y0 y1y1 y2y2 0123456701234567 En At most one I i = 1. (y n-1,.., y 0 ) = I if I i = 1 &  n = 1 0 otherwise. A = 1 if En = 1 and I i s.t. I i = 1 0 otherwise. Description: A

9. Logic Diagram En I1I1 I3I3 I5I5 I7I7 y0y0 I2I2 I3I3 I6I6 I7I7 y1y1

10. I0I0 I1I1 I6I6 I7I7 y2y2 I0I0 I1I1 I6I6 I7I7 A..

11. Priority Encoder Input (I 2 n -1,…, I 0 ) Output (y n-1,…,, y 0 ) (y n-1,…,, y 0 ) = i if I i = 1 & En = 1 & I k = 0 k < I. V Eo = 1 if En = 1 & I i = 0 i, Gs = 1 if En = 1 & i s.t. I i = 1. V E (Gs is like A, and Eo tells us if enable is true or not). y0y0 y1y1 y2y2 0123456701234567 En EoGs

12. Implement a 32-input priority encoder w/ 8 input priority encoders (high bit priority). y 32, y 31, y 30 I 31-24 Eo Gs y 22, y 21, y 20 I 25-16 Eo Gs y 12, y 11, y 10 I 15-8 Eo Gs y 02, y 01, y 00 I 7-0 Eo Gs En