Do as directed.
(a) Convert the Hexadecimal number 3BC into its Binary equivalent
(b) Convert the Binary number 10011010.010101 to its Hexadecimal equivalent.
(c) Convert the Decimal number 345 into Octal number
Answer:
(a) 3BC _{ 16 } to its binary equivalent
3 |
B |
C |
0011 |
1011 |
1100 |
Therefore, 3BC _{ 16 } = 001110111100 _{ 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.
(b) 10011010.010101 _{ 2 } to its hexadecimal equivalent
1001 |
1010 |
0101 |
01 00 |
9 |
A |
5 |
4 |
Therefore, 10011010.010101 _{ 2 } = 9A.54 _{ 16 }
Explanation:
- To obtain the Hexadecimal equivalent of a binary number, digits of binary number should be divided into groups of four digits starting from the rightmost digit for the integer part and starting from the leftmost digit for the fractional part.
- Convert each group of 4 digits to one hexadecimal digit as given in the table below.
- Note: 1,2 or 3 zeroes can be added before the leftmost digit or after the rightmost digit to make a complete group of 4 bits.
(c) 345 _{ 10 } to its octal equivalent
Therefore, 345 _{ 10 } = 531 _{ 8 }
Explanation:
- Repeatedly divide the decimal number by 8 until the quotient becomes less than 8 and record all the remainders.
- The remainders should be written bottom to upwards to get the octal equivalent of the decimal number.