To solve this problem, we need to simplify the Boolean expression \( a = AB \).
- The given Boolean expression is \( a = AB \), where \( A \) and \( B \) are Boolean variables.
We need to determine the simplified or equivalent form of this expression.
- The expression \( a = AB \) is already in its simplest form. There is no need for further simplification because it represents the AND operation between \( A \) and \( B \).
- The expression \( AB \) is already in the minimal sum of products form, and it cannot be simplified any further.
The expression \( a = AB \) is already in its simplest form, and there is no further simplification needed. The equivalent expression is \( AB \).
Match the LIST-I with LIST-II
LIST-I (Logic Gates) | LIST-II (Expressions) | ||
---|---|---|---|
A. | EX-OR | I. | \( A\bar{B} + \bar{A}B \) |
B. | NAND | II. | \( A + B \) |
C. | OR | III. | \( AB \) |
D. | EX-NOR | IV. | \( \bar{A}\bar{B} + AB \) |
Choose the correct answer from the options given below:
Match List-I with List-II:
List-I (Counters) | List-II (Delay/Number of States) |
---|---|
(A) n-bit ring counter | (I) Number of states is \( 2^n \) |
(B) MOD-\(2^n\) asynchronous counter | (II) Fastest counter |
(C) n-bit Johnson counter | (III) Number of used states is \( n \) |
(D) Synchronous counter | (IV) Number of used states is \( 2n \) |
Choose the correct answer from the options given below:
A MOD 2 and a MOD 5 up-counter when cascaded together results in a MOD ______ counter.