1. Decoders Zhijian John Wang

2. What are they?

3. Overview of a decoder A device that reverses the process of an encoder Convert information from one format to another

4. Binary decoders n inputs to 2 n outputs Can be used to generate the 2 n minterms of n input variables Minterm – a product term where each of the n variables appear only once

5. 2x4 decoder F 0 = X'Y' F 1 = X'Y F 2 = XY' F 3 = XY XY Truth table Each output is a 2-variable minterm: (X'Y', X'Y, XY' or XY)

6. 3x8 decoder F 1 = x'y'z xzy F 0 = x'y'z' F 2 = x'yz' F 3 = x'yz F 5 = xy'z F 4 = xy'z' F 6 = xyz' F 7 = xyz Truth table

7. Conversion factor In general, for an n-bit code, a decoder could select up to 2 n lines: : : n-bit code n to 2 n decoder 2 n output lines

8. Decoder expansion Expand a decoder with n inputs to n+1 inputs A0A0 A1A1 A2A2 000 010 001 011 100 110 101 111 A2A1A0A2A1A0

9. Implementing functions

10. A boolean function in sum-of-products form (sum of minterm products) can be implemented using: ▫a decoder to create the minterms ▫OR gates to sum up the minterms Any combinational circuit with n inputs and m outputs can be implemented with an n-to-2 n decoder with m OR gates.

11. 3x8 decoder implementing functions 3x8 Dec S2S1S0S2S1S0 x y z 0123456701234567 S C S = x’y’z + x’yz’ + xy’z’ + xyz C = x’yz + xy’z + xyz’ + xyz

12. 4x16 decoder implementing functions F 1 = A’B’CD + A’BC’D + ABCD F 2 = ABC’D’ + ABCD’ + ABCD F 3 = ?