CENG 24 Digital Design Lecture 2 Amirali Baniasadi amirali@ece.uvic.ca
This Lecture Chapter 6: Registers and Counters 2
Registers Sequential circuits are classified based in their function, e.g., registers. Register: A group of flip-flops each storing one bit of information. Registers include flip-flops and gates: flip-flops hold the information, gates control how the information is transferred to the register. Counter is a register that goes through a predetermined sequence of states. 3
4-bit Register Loads in parallel Clear: Cleans the output to all s. 4
Register with Parallel Load To fully synchronize the system clock signals should arrive at the same time at all flip-flops. Therefore we do not control the clock by gates. Load =, we load data Load =, register content does not change I I I2 I3 5
Register with Parallel Load Load =, register content does not change A A A2 A3 6
Shift Registers A register capable of shifting its binary information in one or both directions is called the shift register. 7
Serial Transfer A digital system is in the serial mode when information is processed one bit at a time. Serial transfer of information from A to B: 8
Remember 4-bit Parallel Adder Circuit? 9
Serial Addition Slower compared to parallel addition, but uses less equipment.
Serial Adder vs. Parallel Adder PA uses registers with parallel load, SA uses shift registers. PA uses more FAs compared to SA. Excluding the registers, PA is a combinational circuit, SA is sequential.
Serial Adder: Design Procedure State Table for a Serial Adder: Present State Inputs Next State Output Flip-Flop inputs Q x y Q S J K x x x x x x 2
Serial 4-bit Parallel Adder Circuit 3
Universal Shift Register A register capable of shifting in both directions and loading in parallel. Stores Information Multiplexer Inputs: : No Change :Shift Right 2:Shift Left 3:Parallel load Controls information transfer 4
Ripple Counters A register that goes trough a prescribed sequence of states is called a counter. There are two groups of counters: Ripple counters and Synchronous counters. Ripple counters: The flip-flop output triggers other flip-flops. Synchronous counters count the clock. 5
Binary Ripple Counter A binary ripple counter consists of a series of complementing flip-flops, with the output of each flipflop connected to the next higher order. Examples of complementing flip-flops are T and D (with the output complement connected to the input) flipflop. Binary Count Sequence A3 A2 A A A is complemented with each count pulse A is complemented when A goes from to A2 is complemented when A goes from to A3 is complemented when A2 goes from to 6
Examples of Binary Ripple Counters 7
Binary Ripple Counter Count-down counter: A binary counter with reverse count: Starts from 5 goes down. In a count-down counter the least significant bit is complemented with every count pulse. Any other bit is complemented if the previous bit goes from to. We can use the same counter design with negative edge flip-flops to make a count-down flip-flop. 8
BCD Ripple Counter A BCD counter starts from ends at 9. 9
Logic Diagram of BCD Ripple Counter Q is applied to the C inputs of Q2 and Q8 Q2 is applied to the C input of Q4 J and K are connected to either or flip-flop outputs 2
Logic Diagram of BCD Ripple Counter Verification: Does the circuit follow the states? Q is complemented with every count (J=K=) Q2 complements if Q goes from to and Q8 is Q2 remains if Q8 becomes Q4 complements if Q2 goes from to Q8 remains as long as Q2 or Q4 is When Q2 and Q4 are, Q8 complements when Q goes from to. Q8 clears and the next Q transition. 2
Three-Decade Decimal BCD Counter Counts from to 999: When Q8 goes from to the next higher order decade is triggered 22
4-bit Synchronous Binary Counters A flip-flop is complemented if all lower bits are. A3 A2 A A 23
4-bit Up-Down Binary Counters In a down binary counter a) The least significant bit is always complemented b) a bit is complemented if all lower bits are. Change an up counter to a down counter: The AND gates should come from the complement outputs instead of the normal one Up =, Down =: Circuit counts up since input comes from Normal output Up =, Down =: Circuit counts down since input comes from Complemented output 24
Binary Counter with Parallel Load Sometimes we need an initial value prior to the count operation. Initial value: I3 I2 I I 25
Binary Counter with Parallel Load Count =, Load = 26
Binary Counter with Parallel Load Count =, Load = I I I I I I2 I2 I3 I3 I 27
BCD counter with parallel load In part a, is detected. In part b, is detected. In part a, LOAD is set to and effective next cycle. In part b, counter is immediately cleared 28
Other Counters: Counters with unused states Present State Next State Flip-Flop Inputs A B C A B C JA KA JB KB JC KC X X X X X X X X X X X X X X X X X X JA=KA=B JB=C, KB= JC=B KC= 29
Other Counters: Counters with unused states What happens if we fall in unused states? In this case, results in. results in. The Counter is self-correcting. 3
Other Counters: Ring Counter A ring counter is a counter with ONLY flip-flop set to at any particular time, all other are cleared. 3
Other Counters: Johnson Counter A 4 flip-flop ring counter that produces 8 states (not 4). 32
Summary Counters & Registers Reading up to page 269 Reminder :Homework 6-Chapter 6 problems 6,7,,5,8,9,23,29 and 3 Due Thursday July 26th. 33