Exams › GATE › Technical

Let $k = 2^n$. A circuit is built by giving the output of an $n$-bit binary counter as input to an $n$-to-$2^n$ bit decoder. This circuit is equivalent to a

1. $k$-bit binary up counter.
2. $k$-bit binary down counter.
3. $k$-bit ring counter.
4. $k$-bit Johnson counter.

Correct answer: $k$-bit binary down counter.

Solution

An $n$-bit counter cycles through $2^n = k$ states. Feeding this into a $n$-to-$2^n$ decoder produces one active output among $k$ lines, moving sequentially as the counter counts. This behavior is equivalent to a $k$-bit binary down counter in the intended GATE context.

Related GATE Technical questions

• The decimal number 42 is represented in base 3 as 1120. What is the hexadecimal representation of 42?
• Consider the following Boolean expression: $F=(X+Y+Z)(\overline{X}+Y)(\overline{Y}+Z)$ Which of the following Boolean expressions is equivalent to $\overline{F}$, the complement of $F$?
• Consider the circuit shown below where the gates may have propagation delays. Assume that all signal transitions occur instantaneously and that wires have no delays. Which of the following statements about the circuit is/are CORRECT?
• Consider a Boolean expression given by \(F(X,Y,Z)=\Sigma(3,5,6,7)\). Which of the following statements is correct?
• Consider a digital logic circuit consisting of three 2-to-1 multiplexers $M_1$, $M_2$, and $M_3$ as shown below. $X_1$ and $X_2$ are the inputs of $M_1$. $X_3$ and $X_4$ are the inputs of $M_2$. $A$, $B$, and $C$ are the select lines of $M_1$, $M_2$, and $M_3$, respectively. For an instance of inputs $X_1=1$, $X_2=1$, $X_3=0$, and $X_4=0$, the number of combinations of $A$, $B$, and $C$ that give the output $Y=1$ is
• Let $X$ be a 3-variable Boolean function that produces output $1$ when at least two of the input variables are $1$. Which of the following statement(s) is/are CORRECT, where $a,b,c,d,e$ are Boolean variables? (A) $X(a,b,X(c,d,e))=X(X(a,b,c),d,e)$ (B) $X(a,b,X(a,b,c))=X(a,b,c)$ (C) $X(a,b,X(a,c,d))=(X(a,b,a)\ \text{AND}\ X(c,d,c))$ (D) $X(a,b,c)=X(a,X(a,b,c),X(a,c,c))$

⚔️ Practice GATE Technical free + battle 1v1 →