Registers and Counters Chapter 6. Registers and Counters A register is a group of flip-flops Each...
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Transcript of Registers and Counters Chapter 6. Registers and Counters A register is a group of flip-flops Each...
Registers and Counters
• A register is a group of flip-flops• Each flip-flop stores one bit of info• A counter is a register that goes through a
predetermined sequence of binary states
Registers4-bit register with • D Flip-flops• Common clock input• Common clear input; when Clear=0
flip-flops reset asynchronous
Register with parallel loadExercise: Explain how this register works. Why is it necessary to feed back to the combinational input circuit? What if this was not done?
Serial additionExercise: Describe how you add two binary numbers by hand. How do you apply this to design a serial adder?Assume you have two n-bit shift registers. Design a circuit that adds one bit at a time and stores the result in one of the shift registers. How do you handle the carries?Hint: you may need one additional flip-flop. Indicate the clock connections of the shift registers and the flip-flop.
Serial adder
Exercise: Explain how this circuit works. Obtain the excitation/input equations for the JK Flip-flop and the equation for the sum .Run an example sum assuming the circuit uses two 3-bit shift registers.
𝐽𝑄=𝑥𝑦
𝐾𝑄=𝑥 ′ 𝑦 ′=(𝑥+𝑦) ′
𝑆=𝑥⨁ 𝑦⊕𝑄
Universal shift register
1. Clear control to clear register to 02. Clock input to synchronize operations3. Shift-right control to enable operation and associated
input and output lines4. Shift-left control to enable operation and associated input
and output lines5. Parallel-load control to enable parallel transfer and the n
input lines6. n parallel output lines7. Control state to leave information in the register
unchanged
Counters
• A counter is a register that goes through a prescribed sequence of states upon the application of input pulses
• Two types of counters– Ripple counters– Synchronous counters
Ripple counters4-bit binary ripple counter with D flip-flops
Exercise: Explain how this counter works.
BCD ripple counterExercise: Obtain the excitation equation and the state table. Explain how this counter works.
Synchronous Counters
• Simple design procedure• Least significant digit Flip-flop is
complemented with every clock pulse• A flip-flop in any other position is
complemented when all the bits in the lower significant positions are equal to 1
Synchronous CountersExercise: Using the excitation tables for the JK flip-flops explain how this counter works.
Up-down binary counter
Countdown binary counter:• Least significant bit is complemented with
each clock pulse• A bit in any other position is
complemented is all lower significant bits are all equal to 0
BCD counter
𝑇 𝑄1=1𝑇 𝑄2=𝑄 ′ 8𝑄1
𝑇 𝑄4=𝑄2𝑄1
𝑇 𝑄8=𝑄8𝑄1+𝑄4𝑄2𝑄1
𝑦=𝑄8𝑄1
Flip-flop input equations are simplified using maps
Binary counter with parallel loadExercise: Explain how this counter works:• When Load is high/low;• When Clear is high/low; • When Count is high/low;• How should Load and
Clear be for counting?
Johnson counter
Connecting complemented LSB to ring counter input doubles the number of states of ring counter.
What happens if counter starts from an unused state?