## Number System Viva Questions

Number System Viva Questions, Short Questions of Number System, Viva Question on Number System, Engineering Viva Questions, Short Questions on Digital Circuit Systems

### Short Questions and Answers

**Q.1.** *What do you mean by a positional-weighted system?*

**Ans.** A positional-weighted system is one in which the values attached to the symbols depend on their location with respect to the radix point.

**Q.2.** *Name some positional-weighted systems.*

**Ans.** Binary, Octal, Decimal, and Hexadecimal are the commonly used positional-weighted number systems.

**Q.3.** *What does the base or radix of a number system indicate?*

**Ans.** The base or radix of a number system indicates the number of unique symbols used in that system. The radix point separates the integer and fraction parts.

**Q.4**. *What do the extreme right and left digits in a number indicate?*

**Ans.** In a number, the extreme left digit is the MSD and the extreme right digit is the LSD.

**Q.5.** *Why is the binary number system used in digital systems?*

**Ans.** The Binary number system is used in digital systems because the devices used in digital systems operate in two states (ON and OFF) and the signals have two levels which are conveniently represented using binary number system.

**Q.6.** How do you convert a decimal number into a number in any other system with base b?

**Ans.** A decimal integer past can be converted into any other system by using the sum of weight method or by repeated division by b. In repeated division by b, the reminders are read from bottom to top. A decimal fraction part can be convened into any other system by using the sum of weights method or by repeated multiplication by b. In repeated multiplication by b, the integers to the left of the radix point are read from top to bottom.

**Q.7.** *What do you mean by a bit?*

**Ans.** A binary digit is called a bit.

**Q.8.** *What do you mean by a nibble?*

**Ans.** Each 4-bit binary group is called a nibble.

**Q.9.** *What do you mean by a byte?*

**Ans.** Each 8-bit binary group is called a byte.

**Q.10.** *Define word.*

**Ans.** A group of bits processed by a digital system at a time is called a word.

**Q.11.** *What do you mean by word length?*

**Ans.** The number of bits used to make a word is called word length.

**Q.12.** *What is the easiest way to convert large decimal numbers into binary and vice versa?*

**Ans.** The easiest way to convert large decimal numbers into binary and vice versa is via the hexadecimal system.

**Q.13.** *What is the easiest way to convert octal numbers to hexadecimal and vice versa?*

**Ans.** The easiest way to convert octal numbers to hexadecimal and vice versa is via the binary system.

**Q.14.** *How is subtraction donned by complement method?*

**Ans.** Subtraction in any number system with base b can be performed by using b’s complement method or (b-1)’s complement method.

**Q.15.** *How are negative numbers represented?*

**Ans.** Negative numbers can be represented in (a) sign-magnitude form or (b) l ‘s ((b- 1 )’s) complement form or (c) 2’s (b’s) complement form.

**Q.16.** *Explain the sign magnitude representation of numbers.*

**Ans.** In the sign magnitude representation of numbers, the MSB is used to represent sign (0 for positive and 1 for negative) and the remaining bits represent the magnitude in straight binary form.

**Q.17.** *What is 1’s complement representation method?*

**Ans.** In 1’s complement representation, the positive numbers are represented exactly in the same form as straight binary representation whereas the negative numbers are represented by subtracting equivalent positive number from (2^{n}-1), where n is the number of bits used, or by complementing each bit of its positive equivalent.

**Q.18.** *What is 2’s complement representation method?*

**Ans.** In 2’s complement representation, the positive numbers are represented exactly in the same way as in straight binary representation, but the negative numbers are represented by subtracting the equivalent positive number from 2^{n} where n is the number of bits used or by adding 1 or its 1’s complement form.

**Q.19.** *How do you obtain the 2’s (b’s) complement of a number?*

**Ans.** The 2’s (b’s) complement of a number can be obtained by adding 1 to the l’s ((b-1)’s) complement of the number.

**Q.20.** *What do you mean by the ‘sign-magnitude’ form of representation?*

**Ans.** The sign-magnitude form of representation is one in which an additional bit called the sign bit is placed in front of the number. If the sign bit is a 0, the number is positive. If it is a 1, the number is negative.

**Q.21.** *What are the characteristics of the 2’s complement numbers?*

**Ans.** The 2’s complement numbers have the following characteristics.

- There is one unique zero.
- The 2’s complement of 0 is 0.
- The leftmost bit cannot be used to express a quantity. It is a sign bit. If it is a 1, the number is negative and if it is a 0, the number is positive.
- For an n-bit word which includes the sign bit, there are 2
^{n-1}– 1 positive integers, 2^{n-1}negative integers and one 0, for a total of 2^{n}unique states. - Significant information is contained in the 1s of the positive numbers and the 0s of the negative numbers.
- A negative number may be convened into a positive number by finding its 2’s complement.

**Q.22.** *What are the three methods of obtaining the 2’s complement of a given binary number?*

**Ans.** The 2’s complement of a binary number can be obtained

- By finding its 1’s complement and adding 1 to it, or
- By subtracting the given N-bit binary number from 2
^{N}, or - By copying down, starting from the LSB all bits up to and including the first 1 and then complementing the remaining bits.

**Q.23.** *How do you perform subtraction using the 2’s complement method?*

**Ans.** In 2’s complement subtraction, add the 2’s complement of the subtrahend to the minuend. If there is a carry out, ignore it. Look at the sign bit, i.e. the MSB of the sum term. If the MSB is a 0, the result is positive and is in true binary form. If the MSB is a 1 (whether there is a carry or no carry at all), the result is negative and is in its complement form. Take its 2’s complement to get the magnitude in binary.

**Q.24.** *How do you perform subtraction using the l’s complement method?*

**Ans.** In 1’s complement subtraction, add the 1’s complement of the subtrahend to the minuend. If there is a carry out, bring the carry around and add it to the LSB. This is called the end around carry. Look at the sign bit (MSB). If the MSB is a 1 (whether there is a carry or no carry at all), the result is negative and is in its l’s complement form. Take its l’s complement to get the magnitude in binary.

**Q.25.** *What do you mean by end around carry? When does it come into picture?*

**Ans.** The process of adding the carry bit to the LSB is called end around carry. It comes into picture in l’s ((b – 1)’s) complement method of subtraction.

**Q.26.** *How are large binary numbers represented?*

**Ans.** Large binary numbers can be represented using double precision or triple precision. Double precision requires two storage locations (registers) to represent each binary number and triple precision requires three.

**Q.27.** *What is the advantage of floating point notation?*

**Ans.** The advantage of floating point notation is – very large and very small binary numbers can be represented very conveniently using this.

**Q.28.** What is the main advantage of octal and hexadecimal systems?

**Ans.** The main advantage of octal and hexadecimal systems is their ease of conversion to and from binary. Also an octal number is 1/3rd of the length of the corresponding binary number and a hex number is 1/4th of the length of the corresponding binary. So, they are short hand representations of binary numbers.

**Q.29.** *Why is hexadecimal code widely used in digital systems?*

**Ans.** Hexadecimal code is widely used in digital systems, because it is very convenient to enter binary data in a digital system using hex code.

**Q.30.** *How do you convert an octal number into binary?*

**Ans.** To convert an octal number into binary, replace each octal digit by its 3-bit binary equivalent.

**Q.31.** *How do you convert binary number into octal?*

**Ans.** To convert a binary number into octal, starting from the binary point make groups of 3-bits on either side of the binary point and replace each 3-bit group by an octal digit. The required number of 0s can be added to the left of the integer part and to the right of the fraction part.

**Q.32.** *How do you convert a binary number into hex?*

**Ans.** To convert a binary number into hex, starting from the binary point make groups of 4-bits on either side of the binary point and replace each 4-bit group by a hex digit.

**Q.33.** *How do you convert a hex number into binary?*

**Ans.** To convert a hex number into binary, replace each hex digit by its 4-bit binary equivalent.