GATE CS & IT Engineering Digital Logic Syllabus

Digital Logic syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Digital Logic in GATE CS & IT Engineering, not a summary of it.

1. 1

   Boolean Algebra

   2 topics

   • Basic Concepts
   • Laws and Theorems
2. 2

   Combinational Circuits

   2 topics

   • Logic Gates
   • Adders and Subtractors
3. 3

   Sequential Circuits

   2 topics

   • Flip-Flops
   • Counters
4. 4

   Minimization

   2 topics

   • Karnaugh Maps
   • Quine-McCluskey Method
5. 5

   Number Representations and Computer Arithmetic

   2 topics

   • Fixed Point Arithmetic
   • Floating Point Arithmetic

Digital Logic flashcards for GATE CS & IT Engineering

18 of 51 cards from the Digital Logic deck — real questions with worked answers.

1. In digital systems, what is the difference between a bit and a nibble, and how many distinct values can an $n$-bit binary number represent?

   A bit is a single binary digit ($0$ or $1$); a nibble is a group of $4$ bits. An $n$-bit binary number can represent $2^{n}$ distinct values, ranging from $0$ to $2^{n}-1$.

2. How do you convert the unsigned binary number $1011_{2}$ to decimal?

   Weight each bit by its positional power of $2$: $1\cdot2^{3} + 0\cdot2^{2} + 1\cdot2^{1} + 1\cdot2^{0} = 8 + 0 + 2 + 1 = 11_{10}$.

3. What is the $2$'s complement representation, and how is the range of an $n$-bit $2$'s complement number expressed?

   The $2$'s complement of a number is obtained by inverting all bits and adding $1$. An $n$-bit $2$'s complement number represents values in the range $-2^{n-1}$ to $2^{n-1}-1$.

4. How are the binary and Gray codes related, and what key property does Gray code possess?

   Gray code is a reflected binary code in which two successive values differ in exactly one bit. To convert binary $b$ to Gray $g$: $g_{i} = b_{i} \oplus b_{i+1}$ (MSB unchanged). This single-bit-change property minimizes errors in transitions.

5. What is the excess-3 (XS-3) code for a decimal digit $d$, and why is it a self-complementing code?

   Excess-3 code is $d + 3$ expressed in $4$-bit binary. It is self-complementing because the $9$'s complement of a digit is obtained simply by taking the $1$'s complement (bitwise NOT) of its XS-3 code.

6. State the difference between weighted and non-weighted codes, giving one example of each.

   In a weighted code each bit position has a fixed numeric weight (e.g., BCD/$8421$, where weights are $8,4,2,1$). In a non-weighted code positions have no fixed weight (e.g., Excess-3 and Gray code).

7. How do you detect overflow when adding two $n$-bit $2$'s complement numbers?

   Overflow occurs when two operands of the same sign produce a result of the opposite sign. Equivalently, overflow $= C_{in} \oplus C_{out}$ of the most significant bit position.

8. State the two basic algebraic laws (commutative and associative) of Boolean algebra for AND and OR.

   Commutative: $A + B = B + A$ and $A \cdot B = B \cdot A$. Associative: $(A+B)+C = A+(B+C)$ and $(A\cdot B)\cdot C = A\cdot(B\cdot C)$.

9. State De Morgan's two theorems in Boolean algebra.

   $\overline{A + B} = \overline{A} \cdot \overline{B}$ and $\overline{A \cdot B} = \overline{A} + \overline{B}$. The complement of a sum equals the product of complements, and vice versa.

10. State the absorption laws of Boolean algebra.

    $A + A\cdot B = A$ and $A\cdot(A + B) = A$. A second form: $A + \overline{A}\cdot B = A + B$ and $A\cdot(\overline{A}+B) = A\cdot B$.

11. What is the consensus theorem in Boolean algebra?

    $A\cdot B + \overline{A}\cdot C + B\cdot C = A\cdot B + \overline{A}\cdot C$. The redundant consensus term $B\cdot C$ can be eliminated. Dual form: $(A+B)(\overline{A}+C)(B+C) = (A+B)(\overline{A}+C)$.

12. State the distributive laws of Boolean algebra.

    $A\cdot(B+C) = A\cdot B + A\cdot C$ and the dual $A + B\cdot C = (A+B)\cdot(A+C)$. Note the second form has no counterpart in ordinary algebra.

13. List the Boolean identity (null, identity, idempotent, and complement) laws.

    Identity: $A+0=A$, $A\cdot1=A$. Null: $A+1=1$, $A\cdot0=0$. Idempotent: $A+A=A$, $A\cdot A=A$. Complement: $A+\overline{A}=1$, $A\cdot\overline{A}=0$.

14. What is the principle of duality in Boolean algebra?

    The dual of any valid Boolean identity is also valid; it is obtained by swapping every $+$ with $\cdot$ and every $0$ with $1$, while keeping all variables unchanged. Example: dual of $A+1=1$ is $A\cdot0=0$.

15. Write the truth table outputs and Boolean expressions for the XOR and XNOR gates of two inputs $A$ and $B$.

    XOR: $Y = A\oplus B = \overline{A}B + A\overline{B}$, output is $1$ when inputs differ. XNOR: $Y = \overline{A\oplus B} = AB + \overline{A}\,\overline{B}$, output is $1$ when inputs are equal.

16. Why are NAND and NOR called universal gates?

    Because any Boolean function (AND, OR, NOT, and hence any logic circuit) can be implemented using only NAND gates or only NOR gates. For example, NOT from NAND: $\overline{A} = \overline{A\cdot A}$.

17. Give the Boolean expressions for a $2$-input NAND and a $2$-input NOR gate.

    NAND: $Y = \overline{A\cdot B}$, output is $0$ only when both inputs are $1$. NOR: $Y = \overline{A+B}$, output is $1$ only when both inputs are $0$.

18. How can the number of gate inputs/levels affect propagation delay, and what is fan-out?

    Each gate level adds propagation delay, so deeper circuits are slower. Fan-out is the maximum number of standard gate inputs a single gate output can reliably drive without degrading logic levels.

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