1. Subject: Digital Electronics
Mgtr: José A. Rumipamba López
RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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3. Is generally equal to the number of states that the counter goes through in each
complete cycle before it recycles back to its starting state.
RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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N is the number of FFs
4. In any counter, the signal at the output of the last FF (i.e., the MSB) will have a
frequency equal to the input clock frequency divided by the MOD number of the
counter.
RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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For example, in a MOD-16 counter, the output from the
last FF will have a frequency of 1/16 of the input clock
frequency
5. RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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6. RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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7. RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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8. RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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9. RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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10. To construct a counter that starts counting from all 0s and has a MOD number of X:
1) Find the smallest number of FFs such that 𝟐 𝑵 ≥ 𝑿, and connect them as a
counter.
2) Connect a NAND gate to the asynchronous CLEAR inputs of all the FFs.
3) Determine which FFs will be in the HIGH state at a count X; then connect the
normal outputs of these FFs to the NAND gate inputs.
RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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11. RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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MOD-14 ripple counter
12. 1) Design and plot a two-bit parallel adder circuit using full adders and registers
with D FFs.
2) Design and plot the logic circuit and state transition diagram of a counter from 1
to 5.
RONNAL TOCCI - DIGITAL SYSTEMS, 10ª EDICIÓN
6.9 Arithmetic Circuits
Mgtr. José A. Rumipamba López
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