5.2 Numbering systems

Question 1

the most common numbering systems are

Answer 1

decimal - base10
binary - base2
octal - base8
hexadecimal - base16

Question 2

decimal (base10) number system has its origin

Answer 2

from counting on the fingers
digit comes from the Latin word digitus which means finger

Question 3

base is the number of different digits including zero in the number system e.g.

Answer 3

octal or base8 = 0 to 7
hexadecimal or base 16 = 0 to F

Question 4

the value of the largest digit of a numbering system is one less than the base

Answer 4

the value of the smallest digit in the number system is zero

Question 5

the standard shorthand form of writing numbers is known as the positional notation

Answer 5

.

Question 6

the most common numbering system used in everyday life

Answer 6

is decimal.
the digit at the far right is called the (LSD) least significant digit
the digit at the far left is called the (MSD) most significant digit

Question 7

octal system is a shorthand method of

Answer 7

representing three-bit binary words

Question 8

binary coded decimal

Answer 8

.

Question 9

the simplest number system employing positional notation is

Answer 9

binary.
has a base of 2
uses just two digits 1 and 0

Question 10

the value of the largest digit of a numbering system is one less than the base. For example, in a binary system (base 2), the largest digit is 1.

Answer 10

.

Question 11

The value of the smallest digit of a numbering system is

Answer 11

zero

Question 12

Gray code is also known as

Answer 12

reflective binary code

Question 13

The binary number system is used in digital electronics because the two basic conditions of electricity, ‘ON’ and ‘OFF’, can be represented by the two digits of the binary number system

Answer 13

ON’, it represents the digit 1, and when it is ‘OFF’, it represents the digit 0.

Question 14

417 in the decimal system. As it is converted digit-by-digit, the first digit is the 4, which in binary is 0100. Second, the 1 is a binary 0001. Finally, the 7 is 0111

Answer 14

That makes the full number 417 in BCD equal to 0100 0001 0111 2

Question 15

when is gray code useful

Answer 15

when rapidly changing values could result in errors due to hardware and interfacing constraints.

Gray codes are used in rotary and optical encoders, Karnaugh maps, and error detection

Question 16

The hamming distance (a metric for comparing two binary data strings) of two neighbouring Gray codes is always

Answer 16

1

Question 17

first Gray code and last Gray code also has hamming distance is always

Answer 17

1 so it is also called cyclic codes

Question 18

In aircraft, where altimeters are normally mechanical, an encoding disk synced to the dials may produce a type of Gray code output

Answer 18

called the Gillham code to send to the transponder for processing

Question 19

Gray code sequences must be converted to what if they are used in mathematical computations or for displays

Answer 19

binary or binary coded decimal (BCD)

Question 20

2 to the power of 0 =

Answer 20

1

Question 21

2 to the power of 1=

Answer 21

2

Question 22

converting decimal to binary step 1.

Answer 22

divide 100 by 2
use quotient obtained in this step as the dividend for the next step
repeat the process until quotient becomes 0
binary equivalent is obtained by reading the remainders from bottom to top as shown below.

Dividend Remainder
100 ÷ 2 = 50 0
50 ÷ 2 = 25 0
25 ÷ 2 = 12 1
12 ÷ 2 = 6 0
6 ÷ 2 = 3 0
3 ÷ 2 = 1 1
1 ÷ 2 = 0 1

answer is = 1100100

Question 23

in converting decimals to binary what is considered the most significant bit (MSB)

Answer 23

The first remainder obtained (at the bottom)

Question 24

in converting decimals to binary what is considered the least significant bit (LSB)

Answer 24

The last remainder (at the top)