Convert FA23D of base 16 to octal number system
Answers
Answer:
Hexadecimal number: - FA23D
F represent 15 , A represents 10 and D represents 13
first web have to convert the given Hexadecimal number into binary and then into octal.
F(15) = 1111 in binary
A(10)= 1010 in binary
2=0010 in binary
3=0011 in binary, and
D(13) = 1101 in binary
so binary equivalent of the given hexadecimal number is
1111 1010 0010 0011
now to convert the binary into octal we have to group the binary in to group of three digits, if the group is not full filled we can add extra zero from left side
001 111 101 000 100 011
now w have to convert the binary into octal
001 = (0*2^2)+(0*2^1)+(1*2^0) =0+0+1 = 1
111 = (1*2^2)+(1*2^1)+(1*2^0) = 4+2+1 = 7
101 = (1*2^2)+(0*2^1)+(1*2^0) = 4+0+1 = 5
Similarly for the rest we get
175043 this the octal of the given Hexadecimal number
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Hexadecimal to Octal
In this type of questions first we have to convert hexadecimal into binary and then binary to octal
hexadecimal to binary
- A = 10
- B = 11
- C = 12
- D = 13
- E = 14
- F = 15
FA23D = 15 10 2 3 13
one by one we will convert each digit in binary
15
2 |15| 1
2 | 7 | 1
2 | 3 | 1
2 | 1 | 1
2 | 0 |
- => 1111
10
2 |10| 0
2 | 5 | 1
2 | 2 | 0
2 | 1 | 1
2 | 0 |
- => 1010
2
2 | 2 | 0
2 | 1 | 1
2 | 0 |
- 10
- it is not of four bit so we have to make it of four bit
- => 0010
3
2 | 3 | 1
2 | 1 | 1
2 | 0 |
- 11
- it is not of four bit so we have to make it of four bit
- => 0011
13
2 |13| 1
2 | 6 | 0
2 | 3 | 1
2 | 1 | 1
2 | 0 |
- => 1101
Binary of FA23D is 1111 1010 0010 0011 1101
Binary to octal
we will divide it in 3 bit
011 . 111 . 010 . 001 . 000 . 111 . 101
011
0×2^2 + 1×2^1 + 1×2^0
0 + 2 + 1
= 3
111
1×2^2 + 1×2^1 + 1×2^0
4 + 2 + 1
= 7
010
0×2^2 + 1×2^1 + 0×2^0
0 + 2 + 0
= 2
001
0×2^2 + 0×2^1 + 1×2^0
0 + 0 + 1
= 1
000
0×2^2 + 0×2^1 + 0×2^0
= 0
111
1×2^2 + 1×2^1 + 1×2^0
4 + 2 + 1
= 7
111
1×2^2 + 0×2^1 + 1×2^0
4 + 0 + 1
= 5
binary to octal 3721075
Hexadecimal to octal
FA23D = 3721075