Question

Number Systems

1. What is a bit? What is a byte? What is the relationship between these two terms?
2. How would you abbreviate the phrase "Megabits per second?" How about Megabytes per second?"
3. Most humans are very familiar with the decimal number system. Computers do all operations in binary. What is the decimal equivalent of binary 11001101? What process can you use to perform this conversion without using a calculator? Demonstrate to the class.
4. What is the binary equivalent of decimal 125? What process can you use to perform this conversion without using a calculator? Demonstrate to the class.
5. What is the whole purpose of using the hexadecimal number system? Is it just another number system to complicate the lives of a computer tech? What is the direct relationship between a binary number and a hexadecimal number?
6. What is the binary equivalent of hexadecimal E9? What process can you use to perform this conversion without using a calculator? Demonstrate to the class.
7. What is the hexadecimal equivalent of binary 11001101? What process can you use to perform this conversion without using a calculator? Demonstrate to the class.
8. How many clock cycles are in each of the following? Kilohertz (KHz), Megahertz (MHz), Gigahertz (GHz)
9. How many bytes are in each of the following? Kilobyte (kB), Megabyte (MB), Gigabyte (GB), Terabyte (TB)

Answer 1

1)
bit is the smallest scale in which computer store the information
Bit are assembled into groups of 8 to form a byte
1 byte = 8 bit

2) Megabits per second : 1 Mega bit per second is 1/8 of 1 MegaByte per second.
Lets say our download speed is 1Mega byte per second that means it allows us to download 1Mega byte file in 1 sec.

Megabits per second = 1Mbps
MegaByte per second = 1MBps

See the difference in character 'b'

3) 11001101

2⁷ x 1 + 2⁶ x 1 +  2⁵ x 0 + 2⁴ x 0 + 2³ x 1+ +  2² x 1+ 2¹ x 0 + 2⁰ x 1
=> 128 + 64 + 8 + 4 + 1
=> 205 in decimal


4) 125

125/2 = 62 with remainder 1
62/2 = 31 with remainder 0
31/2 = 15 with remainder 1
15/2 = 7 with remainder 1
7/2 = 3 with remainder 1
3/2 = 1 with remainder 1
1/2 = 0 with remainder 1


Binary is : 01111101

5) Hexadecimal numbers provide human friendly representation of binary-coded values .
They simplify life of tech and not complicate
They are decoded in group of 4 bits
1 hexadecimal number comprises of 4 bits


6)E9

E in group of 4 bits is 1110
9 in group of 4 is 1001
Hence its 11101001

7)11001101
Separate in bits of 4  1100 & 1101

1100 . is C . and 1101 is D

Hence Hex is CD


8)  kilohertz (kHz) = (1,000 of cycles per second,
the megahertz (MHz) = 1,000,000 of cycles per second
gigahertz (GHz)= 1,000,000,000 of cycles per second.
terahertz (THz)= 1,000,000,000,000 of cycles per second.


9) 1kB = 1024 bytes = 2¹⁰ byte
1MB = 1024 Kbyte = 2²⁰ byte
1GB = 1024 Mbyte = 2³⁰ ​​​​​​​ byte
1TB = 1024 Gb = 2⁴⁰ ​​​​​​​ byte