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 2 n 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 -> 1 Abstract 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 = 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 ALU What 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