Convert 1C6A _{ 16 } to
(a) Decimal
(b) Binary
Answer:
1C6A _{ 16 }
- Decimal
1C6A _{ 16 } = 1 x 16 ^{ 3 } + 12 x 16 ^{ 2 } + 6 x 16 ^{ 1 } + 10 x 16 ^{ 0 }
= 4096 + 3072 + 96 + 10
= 7274 _{ 10 }
Explanation:
- To obtain the decimal equivalent of a hexadecimal number, individual digits of hexadecimal number should be multiplied by powers of 16 starting with rightmost digit multiplied by 16 ^{ 0 } , second last digit multiplied by 16 ^{ 1 } , third last digit multiplied by 16 ^{ 2 } and so on up to the leftmost digit.
- For digits after the decimal point, the leftmost digit should be multiplied by 16 ^{ -1 } and the next digit by 16 ^{ -2 } and so on up to the rightmost digit.
- For alphabets A to F, the corresponding codes should be multiplied with the respective power of 16.
Here,
- A = 10
- B = 11
- C = 12
- D = 13
- E = 14
- F = 15
b. Binary
1C6A _{ 16 }
1 |
C |
6 |
A |
0001 |
1100 |
0110 |
1010 |
Therefore, 1C6A _{ 10 } = 0001110001101010 _{ 2 }
Explanation:
- To obtain the binary equivalent of a hexadecimal number, individual digits of the hexadecimal number should be converted to binary in groups of four digits as given in the table below.