4-3) Identify & Convert Numbers and Symbols

Question 1

How would you write out a 9 digit conversion table for decimal to binary number systems?

Answer 1

Question 2

How would you write out 1 to 15 in binary?

Answer 2

Question 3

How many digits does the decimal system have and what are they?

Answer 3

10

0-9

Question 4

Which number system is a base 10 system?

Answer 4

Decimal

Question 5

How many numbers does the binary number system have and what are they?

Answer 5

2 numbers: 1 and 0

Question 6

Which number system is a base 2 system?

Answer 6

Binary

Question 7

How many numbers does the octal number system have and what are they?

Answer 7

8

0-7

Question 8

Describe the process for converting decimal to octal.

Answer 8

• Divide the number by 8, record the remainder (as a whole number not a decimal)
• Divide the quotient of the first operation by 8 again, record the remainder again as a whole number
• Divide the quotient of the second operation by 8 again, record the remainder again as a whole number
• Repeat this process until the quotient is 0 and the remainder is less than 8
• The last remainder is the most significant digit, the first remainder is the least significant digit
• Read the number from bottom (most signifiant) to top (least significant)

Question 9

Describe the process of dealing with fractional decimal numbers when converting to octal.

Answer 9

• Multiply fractional decimal by 8, note the quotient
• Multiply the remainder by 8, note the quotient
• Multiply the remainder by 8, note the quotient
• Keep multiplying the remainder by 8 until either: you get a whole number or the numbers start to repeat.
• The number is read from the top down

Question 10

Describe the process of converting Octal to Decimal

Answer 10

• Multiply each digit by 8 raised to the power of the digit’s place:
• 1’s = 8⁰
• 10s = 8¹
• 100s = 8²
• 1000s = 8³
• 10,000 = 8⁴
• Take the Octal number and multiply it by 8 raised to the respective power of the digit.
• All all the products together. The sum of the products is the decimal number.
• When encountering fractional octal numbers, multiply by 8^-1 , 8^-2, 8^-3 respectively for the 0.1, 0.01, 0.001 places

Question 11

How many binary digits are needed to represent each of the octal digits?

Answer 11

3

Question 12

Write out the all octal digits in binary

Answer 12

Question 13

Describe the process of converting octal to binary

Answer 13

Each octal number can be represented by 3 binary digits. Convert octal 0-7 to binary 3 digit numbers starting with the most significant digit and ending with the least significant digit.

Question 14

Describe the process of converting binary to octal

Answer 14

Each octal number can be represented by 3 binary digits. Divide the binary number into chunks of 3 binary digits each. Match each 3 digit segment with its respective octal number. Go in the same order of most to least significant digit (left to right).

010111₂ to Octal

010 = 2 (most significant)

111 = 7 (least significant)

010111₂ = 27₈

Question 15

How many digits is hexadecimal based on?

Answer 15

16

Question 16

Write out a chart that shows dec, bin and hex conversions for 0 to 15

Answer 16

Question 17

What is 0 to 15 in Hex?

Answer 17

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Question 18

Describe the process to convert decimal to hex

Answer 18

The process is very similar to converting decimal to octal, but except dividing by 8, you divide by 16.

When the remainder is a whole number less than 16, match that to the corresponding hex number.

Example:

105₁₀ = 69₁₆

105/16 = 6.5625

0.5625 x 16 = 9

=69

Question 19

Describe the process of converting hex to decimal

Answer 19

The process is similar as converting octal to decimal, but instead of multiplying by 8 raised to the digits places (^0, ^1, ^2, ^3, etc. etc.), you multiply by 16 raised to the digits place starting at ^1 for the 1s place and so on. Multiply each hex digit by 16^x and then calculate the sum of these products to get the answer in decimal.

Question 20

What is Binary Coded Decimal?

Answer 20

BCD is a code of 4-bit digits from 0 to 9. Each number from 0 to 9 is represented by a 4-bit digit comprised of 0s and 1s.

Question 21

In binary coded decimal, how are numbers higher than 9 dealt with?

Answer 21

For numbers higher than 9, each digit is broken down into a single digit and represented by their corresponded 4-bit digits.

Question 22

Write out 0 to 9 in BCD

Answer 22

Question 23

What is meant by 8421 code?

Answer 23

8421 is another name for BCD. 8421 are the digits that represent the 4 columns if binary digits in each 4-bit digit:

A 1 in that column represents an 8, 4, 2 or 1, add them together to get the total decimal number that that 4-bit digit represents.

8421

0000= 0

0001 = 1

0010 = 2

0011 = 3

0100 = 4

0101 = 5

0110 = 6

0111 = 7

1000 = 8

1001 = 9