Number System - Binary to decimal, Decimal to binary, Hex to decimal, decimal to hex, hex to octal

1. Logic Building Techniques
and Practices
Number System

2. Hello!

3. Convert the binary number 1011012 to a decimal number
Binary to Decimal Conversion Using Positional Notation Method 1:
the rightmost digit is called the 'Least Significant Bit' (LSB)
the left-most digit is called the 'Most Significant Bit' (MSB)
For a binary number with 'n' digits, the least significant bit has a weight of 20 and the most
significant bit has a weight of 2n-1.

4. express the binary number as a
decimal number: 1011012 = (45)10

5. Binary to Decimal Conversion Using Doubling Method 2
The process of doubling or multiplying by 2.
Step1: in 1011012, the left-most digit is '1'. The double of the previous number is 0. Therefore,
we get ((0 × 2) + 1) which is 1.
Step 2: Continue the same process for the next digit also. The second digit from the left is 0.
Now, double the previous digit and add it with the current digit. Therefore, we get, [(1 × 2) + 0],
which is 2

6. the binary number 1011012 to a decimal using
the doubling method is 4510

7. Practice
110010112 = 20310
101011012= 17310
10112 = 1110
101012 = 2110
1110012 = 5710
11001011012
= 81310
10110101112 = 72710
10000000011002
= 410810
10010100012 = 59310

8. Consectetur nec labore Adipiscingelit sed Sed eiusmod
How to Convert Decimal to Binary?
● Step 1: Divide the given decimal number by 2 and note down the remainder.
● Step 2: Now, divide the obtained quotient by 2, and note the remainder again.
● Step 3: Repeat the above steps until you get 0 as the quotient.
● Step 4: Now, write the remainders in such a way that the last remainder is written
first, followed by the rest in the reverse order.
● Step 5: This can also be understood in another way which states that the Least
Significant Bit (LSB) of the binary number is at the top and the Most Significant Bit
(MSB) is at the bottom. This number is the binary value of the given decimal
number.

9. Convert the decimal number 1310 to binary

10. 16010 = 101000002
1710 = 100012
34 10 = 1000102
244₁₀ =11110100₂
145₁₀ = 10010001₂
112₁₀ = 1110000₂
(8023)10 = (1111101010111) 2
28510 =(100011101)2

11. Convert Hexadecimal to Decimal
The hexadecimal system (shortly hex), uses the number 16 as its base
(radix).
● Obtain the decimal equivalent of hexadecimal from the conversion table.
(table mentioned above)
● Multiply each digit with the power of 16 starting at 0 from the right.
● Add all the numbers together.

12. Convert 7CF (hex) to decimal.
In hexadecimal system,
7 = 7
C = 12
F = 15
7CF = (7 × 162) + (12 × 161) + (15 × 160)
= (7 × 256) + (12 × 16) + (15 × 1)
= 1792 + 192 + 15
= 1999

13. (1DA6)16 = (7590)10
(E8B)16 = (3723)10
(7CA)16 = (1994)10
(80E1)16
=3299310
14516 = (325)10
(10CE)16 = (4302)10
(5BC)16 = (1468)10
(1D9)16 = (473)10

14. Hexadecimal to Octal Conversion
● Conversion of hexadecimal to octal cannot be done directly.
● Firstly we need to convert hexadecimal into its equivalent decimal number then
decimal to octal.
Find the equivalent octal form of C116.
C116 = (C × 161) + (1 × 160)
= C × 16 + 1 × 1
=12 × 16 + 1
= 192 + 1
C116 =193 (Decimal form) Hence, C116 = 3018

15. Method 2
● For each given hexadecimal number digit, write the equivalent binary
number. If any of the binary equivalents are less than 4 digits, add 0’s
to the left side.
● Combine and make the groups of binary digits from right to left, each
containing 3 digits. Add 0’s to the left if there are less than 3 digits in
the last group.
● Find the octal equivalent of each binary group.

16. Convert 1BC16 into an octal number.
1 → 0001, B → 1011, C →1100
Now group them from right to left, each having 3 digits.
000, 110, 111, 100
000→0, 110 →6, 111→7, 100→4
1BC16 = 6748

17. (F)16 = (17)8
(105)16 = (405)8
(7CA)16 = (1994)8
(6C)16
=1548
3EC16 = (1354)8
(2CD)16 = (13158)10
(5BC)16 = (1468)8
(1D9)16 = (473)8

18. (1056)16 to ( ? )8 10126
(2020)10 → (?)16 (7E4)16
(172)10 → ( ? )16
(AC)16
(1032)10 → (?)8
(2010)8

19. Thank you.