In the background is a microprocessor with two useful attributes:
1 Microprocessors are very good at spotting whether a number is zero or not.
2 They contain a series of XOR gates.
So how can it check my number? One easy method is to compare our keyed-in number with the number read from the magnetic strip on the back of the card. Each of our code numbers is treated as a hex number and converted to a four-bit binary number. This results in one 16-bit binary number from the keyboard and another from the magnetic strip on the card, which now have to be compared.
Inside the microprocessor are 16 XOR gates each with two inputs – one from the card and one from the keyboard. Every time the bits coincide, whether they are both zeros or both ones, the output will be a zero.
The 16 results are quickly scanned looking for any output which is not zero. This would indicate an incorrect number. The process is shown in Figure 5.12 but for clarity, only four of the XOR gates have been shown. In real life, there will be 16 of them, of course.
Figure 5.12 Using an XOR gate to compare numbers
The extra bit
The XOR function can be written as ⊕. So, if an XOR gate had inputs called A and B and an output called X, then it would be abbreviated as X=A⊕B.
This is the inverted version of the XOR gate. These result in the output being at logic 1 only when the two inputs have the same value or are equivalent. For this reason, it is often referred to as the Equivalence gate (see Figure 5.13).
Figure 5.13 The truth table for an XNOR or equivalence gate
The tri-state buffer
This looks like a logic gate but behaves more like a switch. In Figure 5.14 we can see that it is quite simple having only an input, an output and another connection called an ‘enable’. The purpose of the enable line is to switch the buffer on or off. When the buffer is switched on, any signal applied to the input appears at the output and when it is switched off, the buffer is disconnected so that there is no output signal present.
Figure 5.14 A tri-state buffer is like a switch
So, why not just use a switch?
The problem with a switch is that, once closed, the input and output are physically joined so that input and output circuits are connected together. The buffer is a one-way device for signals so that the output is isolated from the input to prevent any changes in the next circuit from interfering with the input circuits.
Look for the circles
In the NOT, NAND NOR and XNOR gates a small circle was shown at the output to indicate that the output has been inverted. The same thing occurs with the buffer. If a circle is shown, the output is an inverted copy of the input.
We apply a similar convention to the enable input. If the input has to be a logic 1 level to switch it on, then it is as shown in Figure 5.15. If, however, the enable input has to be a logic 0 to enable it a small circle is shown at the point where the enable line connects with the buffer. When the buffer is switched off, it is said to be disabled. This would give us four possible buffers as in Figure 5.16.
Figure 5.15 An active-low tri-state buffer
Figure 5.16 The four types of tristate buffer
In each case, choose the best option.
1 Which of the gates shown in Figure 5.17 would have an output of logic zero?
(a) A, B, C.
(b) A and D.
(c) B and D.
(d) None of them.
Figure 5.17 Which outputs are at logic 0?
2 If the hex number 4C is applied to eight NOT gates, the output would have the value of:
(a) B3.
(b) 4C.
(c) FF.
(d) CD.
3 Which two-input gate has an output of logic 0 when both inputs are at logic 1:
(a) OR.
(b) AND.
(c) NOT.
(d) XOR.
4 A gate is:
(a) necessary to keep the cattle in the field. (b) always operated from a supply of +5 V.
(c) an electronic circuit with three connecting wires. (d) an electronic switching circuit whose output voltage depends on the inputs.
5 Adding the input and output binary values of a NOT gate:
(a) can be 0, 1 or 2 depending on the inputs.
(b) will give a voltage around 2.5 V.
(c) always results in 1.
(d) is not possible.
6. Registers and memories
The logic gates that we met in the last chapter occur in their millions in microprocessors and in the surrounding circuitry. They are to be found in all microprocessors from the oldest and simplest, to this years’ ‘Ultimate Wonder Child’ and even next year’s ‘New and Improved Ultimate Wonder Child MkII’.
When logic gates are used in a microprocessor, they are usually grouped together into circuits, called flip-flops, each one being able to store a single binary digit.
A flip-flop or bistable is a circuit that can store a single binary bit – either 0 or 1. One useful characteristic of the flip-flop is that it can only have an output of 0 or 1. It cannot hover somewhere in between. The flip-flop is shown in Figure 6.1. The purpose of the clock input is to tell the flip-flop when to accept the new input level.
Figure 6.1 A flip-flop – the basic building block of a microprocessor
The sequence of the events is:
1 Apply the binary level to be stored.
2 Wait a short time (a few nanoseconds) until the voltage is properly established.
3 Apply a signal to the clock input to tell the flip-flop to memorize the signal present at the input.
Why do we have to wait?
When we apply a voltage to a length of wire, we would hope that the voltage changes as in Figure 6.2. Unfortunately, it takes a few nanoseconds to settle down. The rise of voltage travels along the connecting wire and is reflected from the end causing another voltage to be reflected towards the input. This reflection is itself reflected and after repeated reflections, the voltage slowly settles down to its new level as in Figure 6.3. This occurs if we suddenly tip a bucket of water into a half-filled bath. The added water sets up a wave that is reflected backwards and forwards along the bath as the new level is established. If we didn’t wait for the voltage to settle down, we could accidentally store an incorrect value.
Figure 6.2 A voltage is switched on – how we would like it to change
Figure 6.3 A voltage is switched on – what really happens?
And what about the clock signal?
This is just an input to tell the flip-flop that it is time to read the input level. All microprocessor operations are carefully timed by clock pulses to ensure that the system operates in the correct sequence.
The clock signal is usually a positive-going voltage pulse. This pulse can be used to switch two circuits at different times by designing one circuit to respond to an increasing voltage and the other to use a decreasing voltage. If, for example, the pulse in Figure 6.4 were to be 10 ns wide then this could create the required delay for the voltage to settle. The circuit supplying the input voltage is kicked into action by the positive-going edge and then 10 ns later the negative-going edge instructs the flip-flop to save the data present at that time.