Number Systems, Operations, and Codes

Question 1

What symbols are in the binary number system?

Answer 1

0 and 1

Question 2

Convert 100101.01 to decimal

Answer 2

(100101.01)₂ = (1 × 2⁵) + (0 × 2⁴) + (0 × 2³) + (1 × 2²) + (0 × 2¹) + (1 × 2⁰) + (0 × 2⁻¹) + (1 × 2⁻²) = (37.25)₁₀

Question 3

Convert 49 to binary

Answer 3

110001

Question 4

What are all the hexadecimal symbols?

Answer 4

Hex: 0 1 2 3 4 5 6 7 8 9 A B C D E F
Decimal: 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Question 5

What are Octal numbers?

Answer 5

Octal uses the symbols 0 through 7 to represent numbers then carries on from 10 leaving out 8 and 9

Question 6

What is the decimal number 8 as octal?

Answer 6

10

Question 7

What is hexadecimal?

Answer 7

Hexadecimal is a weighted number system. The column weights are powers of 16, which increase from right to left

Question 8

What is Octal

Answer 8

Octal is also a weighted number system. The column weights are powers of 8, which increase from right to left

Question 9

What is Gray Code?

Answer 9

Gray code is an unweighted code that has a single bit change between one code word and the next in a sequence. Gray code is used to avoid problems in systems where an error can occur if more than one bit
changes at a time

Question 10

How is Gray code displayed?

Answer 10

Gray code: Binary:
0000 0000
0001 0001
0011 0010
0010 0011
0110 0100
0111 0101
0101 0110
0100 0111

Question 11

Why can Gray code be better in some scenarios?

Answer 11

As it only has 1-bit changes, it eliminates potential errors