Notes on 3x8 Decoder Lecture

Overview

• A 3x8 decoder has 3 inputs and 8 outputs.
• The inputs are labeled as A, B, and C.
• Outputs are labeled as Y0, Y1, Y2, Y3, Y4, Y5, Y6, Y7.
• There is an additional input called E (enable input).

Block Diagram

• The block diagram illustrates the configuration of a 3x8 decoder.
• The decoder accepts 3 inputs and produces 8 outputs.
• The enable input (E) must be active for the decoder to produce outputs.
  • If E is low (0), the decoder does not produce any outputs (all outputs are inactive).

Truth Table

• Truth table for a 3x8 decoder includes:
  • 3 inputs (A, B, C)
  • 1 enable input (E)
  • 8 outputs (Y0 to Y7)

Key Points from Truth Table:

• If E = 0: Irrespective of inputs (A, B, C), all outputs (Y0 to Y7) are 0.
• If E = 1: Outputs become active based on the combinations of A, B, and C:
  • 000 (A=0, B=0, C=0): Y0 = 1, others = 0 → Y0 = A'B'C'
  • 001 (A=0, B=0, C=1): Y1 = 1 → Y1 = A'B'C
  • 010 (A=0, B=1, C=0): Y2 = 1 → Y2 = A'BC'
  • 011 (A=0, B=1, C=1): Y3 = 1 → Y3 = A'BC
  • 100 (A=1, B=0, C=0): Y4 = 1 → Y4 = AB'C'
  • 101 (A=1, B=0, C=1): Y5 = 1 → Y5 = AB'C
  • 110 (A=1, B=1, C=0): Y6 = 1 → Y6 = ABC'
  • 111 (A=1, B=1, C=1): Y7 = 1 → Y7 = ABC

Logic Circuit

• To derive the formulas for Y outputs, E is included in each output equation:
  • Y0 = E A' B' C'
  • Y1 = E A' B' C
  • Y2 = E A' B C'
  • Y3 = E A' B C
  • Y4 = E A B' C'
  • Y5 = E A B' C
  • Y6 = E A B C'
  • Y7 = E A B C

Components Required:

• NOT Gates for each input A, B, and C to obtain A', B', and C'.
• AND Gates to combine inputs with the enable input E for each output.

Conclusion

• A 3x8 decoder is a many-to-many input-output circuit that converts 3 binary inputs into one of 8 outputs based on the input combinations and the enable signal.