Combinational logic functions and Boolean algebra, logical tables, Karnaugh maps, minimization, solid execution logic and combinational logic functions
Code converter

Logical systems work with binary quantities (1 and 0, H and L, true and false, etc.) there are many binary codes known as BCD code (Binary Coded Decimal).

### Example 4.10

Prepare design for converter between binary code and the seven-segment display unit. Sketch input is shown below. Each segment is marked and lit closing an electrical circuit, i.e. by applying a voltage to the appropriate identically marked wire. Display unit draws 10 digits (0-9). This is ten combinations of output values. The number of output values depends on the number of inputs by Equation (3.1). For three inputs 8 outputs, this is less than required. For four inputs and outputs 16 it is more than the requirement. Consequently, it is necessary to have four input variables, which are identified in the 1 to V4.

Logical table for example is:

| V_4 | V_3 | V_2 | V_1 | a | b | c | d | e | f | g
0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0
1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0
2 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1
3 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1
4 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1
5 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1
6 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1
7 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0
8 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1
9 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1
10 | 1 | 0 | 1 | 0 | x | x | x | x | x | x | x
11 | 1 | 0 | 1 | 1 | x | x | x | x | x | x | x
12 | 1 | 1 | 0 | 0 | x | x | x | x | x | x | x
13 | 1 | 1 | 0 | 1 | x | x | x | x | x | x | x
14 | 1 | 1 | 1 | 0 | x | x | x | x | x | x | x
15 | 1 | 1 | 1 | 1 | x | x | x | x | x | x | x

The first column is the number displayed. Inputs V 1 to V 4 are arranged as a conventional input variable logical table. The right side of this table is found the output values for individual segments. A value of 1 means on, 0 is off and will not affect the value of x solution is needed. In the next step, it is necessary to assemble Karnaugh maps for each segment.

For „a“ segment is :

Expression with value x is equal to expression with value 1. Result function for segment is:

For computed equation exists following scheme:

The same procedure will be created solutions for segments b to g. These blocks are connected to buses in 1 to V 4.