Final answer:
To construct a logic circuit that gives a high output for specific hexadecimal digits, we can use a Karnaugh map to simplify the circuit. The inputs B₈, B₄, B₂, and B₁ represent the bits of the binary equivalent of the digit. We determine the minimized SOP and POS expressions.
Step-by-step explanation:
To construct a logic circuit that gives a high output for specific hexadecimal digits, we can use a Karnaugh map to simplify the circuit. The inputs B₈, B₄, B₂, and B₁ represent the bits of the binary equivalent of the hexadecimal digit. We need the high output for the hexadecimal digits 4, 6, C, and E. By analyzing the Karnaugh map, we can determine the minimized Sum of Products (SOP) and Product of Sums (POS) expressions.
A Karnaugh map can be used to design a logic circuit that outputs a high signal for hexadecimal digits 4, 6, C, or E by simplifying their binary equivalents into minimized SOP and POS expressions.
To design a logic circuit that outputs a high signal for the hexadecimal digits 4, 6, C, or E, first, we must know their binary equivalents. They are 4 (0100), 6 (0110), C (1100), and E (1110). Then, we can construct a Karnaugh map (K-map) for the outputs corresponding to these binary inputs.
For a 4-variable K-map, the minterms for 4, 6, C, and E are m4, m6, m12, and m14, respectively. After placing 1's in these positions on the K-map, we look for ways to group the 1's in order to simplify the expression. The minimized Sum of Products (SOP) expression would be obtained by combining adjacent groups of 1's, while the Product of Sums (POS) expression is obtained by grouping 0's and finding the complement.
The SOP could be B8'B4B2'+B8B2B1', while the POS might be (B8+B2'+B1)(B4'+B2+B1'). Remember, the prime ' symbol indicates the negation of the variable.