# Overview

Digital logic is the study and application of the fundamentals in digital (binary) electronics, e.g. gates, flip-flops, state machines.

# Child Pages

 Logic GatesContentsOverviewD Flip-FlopsImportant ParametersTriggering Overview When sourcing logic IC’s, note that the standard prefix used by many manufactures is “74”. Logic gate inputs are normally labelled as a single letter, starting with A (e.g. a three input AND gate would have inputs A, B and C). The output is normally labelled Y, unless you are using … Continue reading Logic Gates Metastability And SynchronisationContentsFlip-flop MTBF Flip-flop MTBF $${\rm MTBF}(t_r) = \frac{e^{ \frac{t_r}{\tau} } } {T_O fa}$$ where: $$t_r$$ = resolution time (time since clock edge), $$s$$ $$f$$ = sampling clock frequency, $$Hz$$ $$a$$ = asynchronous event frequency, $$Hz$$ $$\tau$$ = flip-flop time constant (this is a funciton … Continue reading Metastability And Synchronisation

# Karnaugh Maps

Karnaugh maps are a way of simplifing combinational logic, often used before realising a combination equation into a number of gates to reduce the complexity.

# Logic Simulators

CEDAR Logic Simulator is my personal favourite. Free, easy to use, colours the wires depending on their state, and allows for named nets as well as direct connections.

# Example Logic Circuits

## 6-State Binary Counter

Category: Counter
Expression Style: Sum of Products
No. of Gates: 14
No. of Flip-flops:  3
1-Bit Inputs: 2 + reset
1-Bit Outputs: 3
Tested On:

• Simulation:
• Hardware: Yes

The 6-state binary counter is a counter which counts from 000 to 101 in the normal binary fashion before resetting back to 0. The output increments on every rising-edge of the count pulse, and the direction pin (upNDown) determines the count direction (when upNDown = 1, the counter goes from 000 to 101, when upNDown is 0 the counter goes from 101 to 000).

The flip-flop equations expressed as sums of products are:

$$Q_2 = \bar{Q_2}.\bar{Q_1}.\bar{Q_0}.\bar{y} + \bar{Q_2}.Q_1.Q_0.y + Q_2.\bar{Q_1}.Q_0.\bar{y} + Q_2.\bar{Q_1}.\bar{Q_0}.y \\ \\ Q_1 = \bar{Q_2}.\bar{Q_1}.Q_0.y + \bar{Q_2}.Q_1.\bar{Q_0}.y + \bar{Q_2}.Q_1.Q_0.\bar{y} + Q_2.\bar{Q_1}.\bar{Q_0}.\bar{y} \\ \\ Q_0 = \bar{Q_2}.\bar{Q_0} + Q_2.\bar{Q_1}.\bar{Q_0} \\ \\$$

## 3-Bit Grey Encoded Counter

Category: Counter
Expression Style: Sum of Products
No. of Gates: 14
No. of Flip-flops: 3
1-Bit Inputs: 2 + reset
1-Bit Outputs: 3
Tested On:

The 3-Bit Grey Encoded Counter is a counter that counts from 0 to 7 in binary in a grey encoded fashion. The counter increments on every rising edge of the bit ‘count’ and the direction bit ‘upNDown’ determines the direction of counting.