Question

Exercises:
1. Explain the types of Numbering system with its base.
2. What is Decimal equivalent of (10111. ID2)?
3. Convert the followings from one base to another base.
a) (A73.A) 16 = (?)10
b) (123.25): = (?)10
c) (351.27)3 = (?)2
d) (33.625) 10 = (?)2​

Answer 1

Answer:

The Octal Numbering System is very similar in principle to the previous hexadecimal numbering system except that in Octal, a binary number is divided up into groups of only 3 bits, with each group or set of bits having a distinct value of between 000 (0) and 111 ( 4+2+1 = 7 ).

Octal numbers therefore have a range of just “8” digits, (0, 1, 2, 3, 4, 5, 6, 7) making them a Base-8 numbering system and therefore, q is equal to “8”.

Then the main characteristics of an Octal Numbering System is that there are only 8 distinct counting digits from 0 to 7 with each digit having a weight or value of just 8 starting from the least significant bit (LSB). In the earlier days of computing, octal numbers and the octal numbering system was very popular for counting inputs and outputs because as it works in counts of eight, inputs and outputs were in counts of eight, a byte at a time.

As the base of an Octal Numbers system is 8(base-8), which also represents the number of individual numbers used in the system, the subscript 8 is used to identify a number expressed in octal. For example, an octal number is expressed as:  2378

Just like the hexadecimal system, the “octal number system” provides a convenient way of converting large binary numbers into more compact and smaller groups. However, these days the octal numbering system is used less frequently than the more popular hexadecimal numbering system and has almost disappeared as a digital base number system.