Computer Organization & Programming

Chapter4

Combinatorial Components

Some common, useful combinatorial circuits

Multiplexor• Some number (power of 2) of inputs and some control inputs

• The current values on the control lines are interpreted as a binary representation of the number of one of the other inputs. That input is passed through to the output.

Demultiplexor• Reverse of the multiplexor

• Single input is routed to one of a number (power of 2) output lines, depending on the control lines.

Decoder• Takes an n-bit input number and uses it to select exactly one of 2n

output lines• note difference between demultiplexor and decoder• The selected output line will have a 1, not a selected input value.

Comparator• outputs a 1 if two input values are equal, 0 otherwise

Comparator

All the As represent one input word, all the Bs represent another input word. The output will be one only if the two inputs are the same

Mux (multiplexer) 2 -> 1

Mux 2 -> 1 implementation

Mux 4 -> 1

Mux 8 -> 1Abstract representation of a multiplexor. The circuit details are hidden, but the essentials are visible.

Implement a Boolean Function using Mux

Decoder 3->8

Decoder circuit

Decoder 4 -> 16

Implement a Boolean Function using Decoder

Shifter

C determines if the shift will be left or right.

Assume D = 10000110. Show exactly what passes through each gate, and what ends up in S.

Half Adder

Called a half adder because it does not do the whole job: it does not add a carry in.

Full Adder

Example – 4bit Adder

Example – 4bit Adder/Subtractor

ALU Slice

1bit ALUWhat happens if F= 11, A=1, B=1, carry in = 1

What happens if F= 10, A=1, B=1, carry in = 1

Note INVA (Inverse A), ENA (Enable A), ENB (Enable B)

Once we have the circuit understood, note the inputs and the outputs. We can hide the rest of the details in using this device.

8Bit ALU

Overflow

ALU with overflow detection