Number Systems: 45 MCQs with answers

16

Hexadecimal is a base-16 number system, using digits 0-9 and letters A-F.

1010

Decimal 10 in binary is 1010 because $1 \times 2^3 + 0 \times 2^2 + 1 \times 2^1 + 0 \times 2^0 = 8 + 0 + 2 + 0 = 10$.

The sign of the number (0 for positive, 1 for negative)

In sign-magnitude representation, the most significant bit (leftmost) is the sign bit: 0 indicates positive and 1 indicates negative. The remaining bits represent the magnitude.

Integer representation

Fixed-point representation has a fixed number of digits after the decimal point. Integer representation is a type of fixed-point where the decimal point is fixed at the right end.

Unicode

Unicode is a universal character encoding standard designed to support the characters of all major world languages, unlike ASCII or EBCDIC which are limited.

A

Binary 1010 equals decimal 10, which is represented as A in hexadecimal.

It is a 7-bit code

Standard ASCII is a 7-bit character encoding, allowing 128 different characters. Extended ASCII uses 8 bits.

True

The binary system is base-2 and uses only the digits 0 and 1.

2

The binary number system is based on 2, which means it uses two digits: 0 and 1.

101

The binary representation of the decimal number 5 is 101.

American Standard Code for Information Interchange

ASCII stands for American Standard Code for Information Interchange, which is a character encoding standard.

13

The binary number 1101 is equal to the decimal number 13.

Uses digits from 0 to 7

The octal number system uses digits from 0 to 7.

Hexadecimal

The digit 'F' is used in the hexadecimal number system, representing the decimal value 15.

1110

The 2's complement of 0010 is 1110, which is obtained by inverting the bits and adding 1.

Binary Coded Decimal (BCD)

Binary Coded Decimal (BCD) is a character encoding scheme that represents decimal numbers in binary.

Base 16

The hexadecimal number system is based on 16, using digits 0-9 and letters A-F.

8

The octal number 10 is equal to the decimal number 8.

10

The decimal number system is based on 10, using digits from 0 to 9.

1101

The binary number system only uses the digits 0 and 1, making '1101' a valid binary number.

F

In the hexadecimal system, the decimal number 15 is represented as 'F'.

Uses digits 0 and 1

The binary number system exclusively uses the digits 0 and 1.

Binary Coded Decimal

BCD stands for Binary Coded Decimal, which represents decimal numbers in binary form.

10

The binary number '1010' is equal to the decimal number 10.

BCD

BCD is not a character encoding scheme; it is a way to represent decimal numbers in binary.

8

The octal number system is based on 8, using digits from 0 to 7.

Hexadecimal

The digit 'A' is used in the hexadecimal number system to represent the decimal value 10.

1010

BCD (Binary Coded Decimal) uses only the binary patterns 0000 to 1001 to represent decimal digits 0-9. The pattern 1010 represents decimal 10, which is not a single decimal digit, so it is invalid in BCD.

0101

The 1's complement is obtained by flipping each bit: 1 becomes 0 and 0 becomes 1. So 1010 becomes 0101.

0100

The 2's complement is found by taking the 1's complement (0011) and adding 1, giving 0100.

15

Octal 17 equals $1 \times 8^1 + 7 \times 8^0 = 8 + 7 = 15$ in decimal.

A code used to detect and possibly correct errors in data transmission or storage

Error codes are used to detect and correct errors that may occur during data transmission or storage. Examples include parity bits and Hamming codes.

The position of the binary point

In floating-point representation, the exponent indicates the position of the binary point (or decimal point) relative to the mantissa, allowing representation of very large or very small numbers.

True

In 1's complement, positive zero is represented as all 0s (e.g., 0000) and negative zero as all 1s (e.g., 1111), leading to two distinct representations for zero.

1101

The binary representation of the decimal number 13 is obtained by converting it to binary, which results in 1101.

Hexadecimal

The hexadecimal number system uses base 16, which includes digits from 0 to 9 and letters A to F.

Unicode Transformation Format - 8 bits

UTF-8 stands for Unicode Transformation Format - 8 bits, which is a variable-width character encoding.

1010

The 1's complement of a binary number is obtained by flipping all bits. For 0110, the 1's complement is 1001.

0111

In Binary-Coded Decimal (BCD), the decimal number 7 is represented as 0111.

47

The hexadecimal number 2F converts to decimal as follows: $2 \times 16^1 + 15 \times 16^0 = 32 + 15 = 47$.

The value of the number

In floating-point representation, the significand (or mantissa) represents the value of the number, while the exponent scales it.

1101

To find the 2's complement, first take the 1's complement (0100) and add 1, resulting in 1101.

Binary is base 2, while decimal is base 10.

Binary is a base 2 number system, while the decimal system is base 10.

57

To convert binary 101101 to octal, group the binary digits in sets of three from the right: 101 101, which is 5 7 in octal.

1011

To represent -5 in 4-bit 2's complement: first write +5 as 0101, then take 1's complement (1010) and add 1, giving 1011.