Number System and Code Convertions · Digital Circuits · GATE ECE

A machine has a 32-bit architecture with 1-word long instructions. It has 24 registers and supports an instruction set of size 40. Each instruction has five distinct fields, namely opcode, two source register identifiers, one destination register identifier, and an immediate value. Assuming that the immediate operand is an unsigned integer, its maximum value is __________.

In a number system of base $r$, the equation $x^2 - 12x + 37 = 0$ has $x = 8$ as one of its solutions. The value of $r$ is _______.

A digital transmission system uses a $(7,4)$ systematic linear Hamming code for transmitting data over a noisy channel. If three of the message-code word pairs in this code ( $m_i ; c_i$ ). Where $c_i$ is the codeword corresponding to the $i^{\text {th }}$ message $m_i$, are known to be $(1100 ; 0101100),(1110 ; 001 1110)$ and $(0110 ; 1000110)$, then which of the following is a valid codeword in this code?

What is the 10 's complement of $(47)_{10}$ ?

$P, Q$ and $R$ are the decimal integers corresponding to the 4-bit binary number 1100 considered in signed magnitude, 1 's complement and 2 's complement representation, respectively. The 6 -bit 2 's complement representation of ( $P+Q+R$ ) is