Technology
The Technology domain in this GATE XH guide tests digital logic, data representation, basic algorithm analysis, and layered system reasoning. You need to move confidently between a truth table, a Boolean expression, a circuit, and a complexity statement.
Core rules and concepts
- Boolean identities include A + A' = 1, A·A' = 0, absorption A + AB = A, and De Morgan's laws (AB)' = A' + B', (A + B)' = A'B'.
- In n-bit two's complement, the range is −2^(n−1) to 2^(n−1) − 1; negation is invert all bits and add 1.
- Combinational outputs depend only on current inputs; sequential outputs depend on state and clocking.
- Big-O ignores constant factors and lower-order terms: 3n² + 5n + 7 is O(n²).
- In layered networks, encapsulation adds headers at each layer and peer layers communicate logically.
Worked example
Simplify F = A'B + AB + A'B'. Group the first and third terms: A'B + A'B' = A'(B + B') = A'. Now F = A' + AB. By absorption, A' + AB = A' + B. A quick check: when A = 0, F = 1; when A = 1, F = B. The simplified expression matches both cases.
Traps that cost marks
Do not confuse the number of n-bit patterns, 2^n, with the signed range. In Boolean work, apply De Morgan's laws to the whole complemented expression, not term by term. In complexity questions, do not drop a dominant term or treat average and worst case as identical. In sequential logic, remember that a clock edge matters; in networking, do not skip the encapsulation order.