In digital technology, the transmitted, received or converted information is expressed by a set of symbols of the binary number system - a binary code.

Any decimal number familiar to us can be represented as a set of ones and zeros of this system. The decimal number 7, for example, in the binary system is written like this: 0111. Here, the leftmost character is the most significant bit, and the rightmost character is the least significant bit of a four-bit binary code number. The translation of this binary number into a decimal number is performed in the following order: 0111=0X2³+1X2²+1X2¹+1x2⁰ =0+4+2+1 =7.

The basis for converting a binary number to decimal is the number 2. The code itself in this case is called the binary natural or code 8-4-2-1.

Table 1 will help you convert decimal numbers to binary and vice versa within a four-digit code.

Table 1

In order to more firmly fix in memory the principle of encoding digital information in a binary system, we propose to experimentally analyze the operation of a four-bit binary counter, assembled, for example, on JK flip-flops according to the circuit shown in Fig. one.

Rice. 1 Four-digit counter

Mount all parts of the counter on the breadboard. Connect LEDs or other indicators to the direct outputs of all triggers, by which it would be possible to visually observe the logical states of the triggers. The function of a source of input counting pulses of long duration is performed by an RS flip-flop assembled on logical elements 2I-NOT DD1.1, DD1.2 and controlled by the SB1 button.

Prepare a table (Table 2) in which you will record the logical states of the triggers of the pulse counter with the symbols of the binary number system. In the leftmost column "Count" immediately write down the sequence numbers of input pulses from 0 to 15. In the second column from the left (Q1) write down the logical state of the first trigger at each next pulse, in the third column (Q2) - the logical state of the second trigger, etc. d.

So, check the installation, the reliability of soldering and, if you do not find any errors, turn on the power. In this case, some LEDs may light up, signaling that the triggers related to them were in a single state at the time of power-up. Press the SB2 button to. apply a low-level voltage to the input R of the triggers and thereby set all the triggers of the counter to the zero state. Now all indicators are off. This logical state of all flip-flops of a four-digit pulse counter is indicated in the table by zeros.

Table 2

Now briefly press and release the SB1 button. In this case, the RS-trigger will switch from the zero state to the single state itself and, by means of a high-level voltage at the direct output, will switch the first trigger of the counter to the same state. As a result, the HL1 LED will turn on. The remaining triggers of the counter will keep the zero state, and their LEDs, of course, should not shine.

Record this state of the triggers in the table: in the Ql-1 column, in the rest-0. Press the second time on the SB1 button, simulating the second input pulse. Immediately the first LED will go out and the second one will turn on - HL2. Now the second trigger is in the single state, and the rest are in the zero state. Write these logical states of the flip-flops to the line corresponding to the second input pulse.

The third input pulse will again set the first trigger of the counter to a single state and will not change the state of the second trigger, so the indicators HL1 and HL2 will light up. In the table, write down this state of the counter in the following form: 1100. At the fourth input pulse, only the HL3 LED will light, and the entry 0010 should appear in the table.

So, slowly, by pressing the SB1 button and reading by the glow of the trigger status indicators, you will gradually fill in the entire table of logical states of the four-digit counter. After that, disconnect the RS-trigger from the input of the counter and apply a sequence of pulses to it from the generator, following at a frequency of 1 ... 2 Hz. The order of plowing the indicators, which at such a frequency can be traced, will confirm your records characterizing the operation of a binary four-digit counter.

Let's summarize. The first trigger of your advanced counter is the LSB, and the fourth is the MSB of the four-digit counter. Accordingly, the columns of symbols of logical states of triggers are located in the table. But in the binary system, the characters of the lower digits in relation to the older ones are located on the right side. Therefore, in order to determine the code state of the counter from the table you compiled for each of the fifteen input pulses, the entries in it should be read from right to left or the table should be flipped in a mirror.

The result is: at the first input pulse - 0001, at the second - 0010, at the third - 0011, etc. until the fifteenth pulse, when the code state of the counter is 1111, after which the pulse count is repeated. In short, this meter status code table, but of course upside down..

Similar experiments with the corresponding outputs can, of course, be carried out with a four-digit counter on D-flip-flops, connecting their inverse outputs to the D inputs so that the flip-flops work in counting mode. It is useful to conduct such a study with the K155IE2 chip. Turning it on according to the scheme shown in Fig. 2, it is possible to compile a table of code states of such a pulse counter from 0 to 9.

Rice. 2 Experience with the K155IE2 chip

As you already know, the maximum decimal number that can be expressed in binary four-digit code is 15. And if this number is three-digit, for example, 137? In binary code, it will look cumbersome and not always convenient for processing: 10001001. Therefore, in digital technology, in addition to binary code, they also use binary-decimal code, where each digit of a decimal number is represented in binary form. With binary coded decimal code, the same three-digit number 137 looks like this:

And how are the binary or binary-decimal code states of the pulse counters translated into digits of the decimal number system? This is done with the help of decoders and sign-synthesizing indicators.

See other articles Section Beginner radio amateur.

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