Number System and Code Convertions · Digital Circuits · GATE ECE
Marks 1
1
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 __________.
GATE ECE 2024
2
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 _______.
GATE ECE 2024
3
The number of bytes required to represent the decimal number 1856357 in packed BCD
(Binary Coded Decimal) form is __________ .
GATE ECE 2014 Set 2
4
X = 01110 and Y = 11001 are two 5-bit binary numbers represented in two’s
complement format. The sum of X and Y represented in two’s complement format
using 6 bits is:
GATE ECE 2007
5
Decimal 43 in Hexadecimal and BCD number system is respectively
GATE ECE 2005
6
The range of signed decimal numbers that can be represented by 6-bite 1’s
complement number is
GATE ECE 2004
7
4-bit 2’s complement representation of a decimal number is 1000. The number is
GATE ECE 2002
8
The 2’s complement representation of –17 is
GATE ECE 2001
9
An equivalent 2’s complement representation of the 2’s complement number
1101 is
GATE ECE 1998
10
A signed integer has been stored in a byte using the 2's complement format. We
wish to store the same integer in a 16-bit word. We should
GATE ECE 1997
11
2’s complement representation of a 16-bit number (one sign bit and 15
magnitude bits) is FFFI. Its magnitude in decimal representation is
GATE ECE 1993
12
The subtraction of a binary number Y from another binary number X, done by adding the 2's complement of Y to X, result in a binary number without overflow. This implies that the result is:
GATE ECE 1987
Marks 2
1
A new Binary Coded Pentary (BCP) number system is proposed in which every
digit of a base-5 number is represented by its corresponding 3-bit binary code.
For example, the base-5 number 24 will be represented by its BCP code 010100.
In this numbering system, the BCP code 100010011001 corresponds to the
following number in base-5 system
GATE ECE 2006
2
11001, 1001 and 111001 correspond to the 2’s complement representation of
which one of the following sets of number?
GATE ECE 2004