Final answer:
A minterm is a term that represents a specific combination of inputs in Boolean algebra, while a maxterm is a term that represents a specific combination of inputs. Overflow refers to a situation where the result of a mathematical operation exceeds the maximum value that can be represented. XOR gate can be implemented using only NAND gates. Sign-magnitude binary numbers can be converted to decimal by considering the leftmost bit. The logic circuit of JK Flip-Flop can be represented using logic gates.
Step-by-step explanation:
(a) Minterm and Maxterm:
A minterm is a term in Boolean algebra that represents a single combination of inputs that produces a specific output. It is the product of all the input variables, with each variable being either complemented (denoted by a bar over the variable) or non-complemented (no bar over the variable).
For example, in the expression AB’C, the term BC is a minterm because it produces an output of 1 when B is true and C is false.
On the other hand, a maxterm is a term in Boolean algebra that represents a single combination of inputs that produces a specific output. It is the sum of all the input variables, with each variable being either complemented or non-complemented.
For example, in the expression (A+B’+C’), the term (A’B’C’) is a maxterm because it produces an output of 0 when A, B, and C are all false.
(b) Overflow:
Overflow refers to a situation in which the result of a mathematical operation exceeds the maximum value that can be represented by the chosen number of bits.
In the context of representing positive and negative numbers, overflow can occur when the result of adding or subtracting two numbers with the same sign produces a result with a different sign.
(c) XOR using NAND gates:
The XOR logic gate can be implemented using only NAND gates. The XOR gate produces a true output only when the number of true inputs is odd.
To implement XOR using NAND gates, we can connect NAND gates in a specific arrangement. The circuit would look like:
(d) Equivalent decimal of sign-magnitude binary numbers:
(i) The sign-magnitude binary number is 01000100. Since the leftmost bit is 0, the number is positive. So, the equivalent decimal is 68.
(ii) The sign-magnitude binary number is 10110011. Since the leftmost bit is 1, the number is negative. So, we can simply convert the magnitude bits, which are 0110011, to decimal, which is 27. The result is -27.
(e) Logic circuit of JK Flip-Flop:
A JK flip-flop is a sequential logic circuit that can store one bit of information. It has two inputs, J (for set) and K (for reset), and two outputs, Q and Q'.
The logic circuit of a JK flip-flop can be represented using logic gates. Here is the circuit: