Convert the following numbers:
i) (F 329)10 in to Binary
ii) (1526.32)10 in to hexadecimal
iii) (736.4)8 in to Decimal
i) Convert (F 329)10 in to Binary
To convert a decimal number to binary, you can repeatedly divide the decimal number by 2 and note the remainders. Reading the remainders from bottom to top gives the binary representation.
| Division | Quotient | Remainder |
|----------------|----------|-----------|
| 329 ÷ 2 | 164 | 1 |
| 164 ÷ 2 | 82 | 0 |
| 82 ÷ 2 | 41 | 0 |
| 41 ÷ 2 | 20 | 1 |
| 20 ÷ 2 | 10 | 0 |
| 10 ÷ 2 | 5 | 0 |
| 5 ÷ 2 | 2 | 1 |
| 2 ÷ 2 | 1 | 0 |
| 1 ÷ 2 | 0 | 1 |Reading the remainders from bottom to top, the binary representation of 329 is 101001001.
Therefore, (F329)10 in binary is 101001001.
ii) Convert (1526.32)10 in to hexadecimal
For the integer part, convert 1526 to hexadecimal:
| Division | Quotient | Remainder (Hexadecimal) |
|----------------|----------|--------------------------|
| 1526 ÷ 16 | 95 | 6 |
| 95 ÷ 16 | 5 | F |
| 5 ÷ 16 | 0 | 5 |Reading from bottom to top, the hexadecimal representation of the integer part is 5F6.
For the fractional part, convert 0.32 to hexadecimal:
| Multiplication | Result | Result (Hexadecimal) |
|----------------|----------|-----------------------|
| 0.32 × 16 | 5.12 | 5 |
| 0.12 × 16 | 1.92 | 1 |
| 0.92 × 16 | 14.72 | E |Combining the results, (1526.32)10 in hexadecimal is 5F6.E.
iii) Convert (736.4)8 in to Decimal
To convert an octal number to decimal, you can use the positional value of each digit.
(736.4)8 =7×82+3×81+6×80+4×8−1
=448+24+6+0.5
=478.5
Therefore, (736.4)8 in decimal is 478.5.