CS355 Sylabus

One-to-many switch: decoder

The decoder is not actually a real one-to-many switch, but it is used for the purpose of selecting one register out of a set (many) of registers.
So in that role (selecting one out of many), it can be used as a one-to-many switch in the construction of the CPU.
Later, I will show you a real one-to-many digital switching device called "demultiplexor". This device can be found in telephone and network equipments that redirect one stream onto one of its many outputs.
Schematically, a decoder has N control signals and 2^N output signals.
At any time, exactly one output signal is equal to 1 (and all other outputs are equal to 0) and the output signal that is 1 depends on the current values of the control signals.
The following figure shows schematically what a 2x4 decoder does. The 2x4 decoder has 2 control signals and 4 outputs:
The following figure shows how a 2x4 decoder can be constructed using elementary gates:
- The construction is very simple, just make sure you remember that an AND gate outputs 1 only when ALL its inputs are equal to 1.
- You connect the inputs of the and-gates to every possible combinations of the input signals:
  - (c₁) (c₀)
  - (c₁) (NOT c₀)
  - (NOT c₁) (c₀)
  - (NOT c₁) (NOT c₀)
- The right figure shows that when what happens when the control signals c₁ = 1 and c₀ = 0. In this case, c₁ = 1 and (NOT c₀ = 1), so that the second AND gate will receive all 1's as inputs. Only this and gate will output 1, and all other and gates will output 0.

Here is a logic-sim circuit file that implements a 2x4 decoder: click here

/home/cs355001/bin/cs355sim /home/cs355001/demo/circuits/decoder