List of top Digital Logic Questions

If \( x \) and \( y \) are two decimal digits and \( (0.1101)_2 = (0.8xy5)_{10} \), the decimal value of \( x + y \) is \(\underline{\hspace{2cm}}\).

Suppose we want to design a synchronous circuit that processes a string of 0's and 1's. Given a string, it produces another string by replacing the first 1 in any subsequence of consecutive 1's by a 0. Consider the following example.
Input sequence: 00100011000011100
Output sequence: 00000001000001100
A Mealy Machine is a state machine where both the next state and the output are functions of the present state and the current input. The above mentioned circuit can be designed as a two-state Mealy machine. The states in the Mealy machine can be represented using Boolean values 0 and 1. We denote the current state, the next state, the next incoming bit, and the output bit of the Mealy machine by the variables $s$, $t$, $b$ and $y$ respectively. Assume the initial state of the Mealy machine is 0. What are the Boolean expressions corresponding to $t$ and $y$ in terms of $s$ and $b$?

Consider a Boolean function \( f(w,x,y,z) \) such that 
$f(w,0,0,z) = 1 $
$f(1,x,1,z) = x + z $
$f(w,1,y,z) = wz + y $

The number of literals in the minimal sum-of-products expression of \( f \) is \(\underline{\hspace{2cm}}\).

Let the representation of a number in base 3 be 210. What is the hexadecimal representation of the number?
Consider the following representation of a number in IEEE 754 single-precision floating point format with a bias of 127.
\[ S : 1 E : 10000001 F : 11110000000000000000000 \] Here \( S \), \( E \), and \( F \) denote the sign, exponent, and fraction components of the floating-point representation.
The decimal value corresponding to the above representation (rounded to 2 decimal places) is \(\underline{\hspace{2cm}}\).

Consider a 3-bit counter, designed using T flip-flops, as shown below. Assuming the initial state of the counter given by $PQR$ as $000$, what are the next three states? 

Assume that a 12-bit Hamming codeword consisting of 8-bit data and 4 check bits is $d_8 d_7 d_6 d_5 c_8 d_4 d_3 d_2 c_4 d_1 c_2 c_1$, where the data bits and the check bits are given in the following tables. Which one of the following choices gives the correct values of $x$ and $y$? 

Consider the following Boolean expression. \[ F = (X + Y + Z)(\overline{X} + Y)(\overline{Y} + Z) \] Which of the following Boolean expressions is/are equivalent to $\overline{F$ (complement of $F$)?}
Which one is false ?
Choose the correct option: \((224)_5\)
Largest among all in a single precision