Question

convert the following real numbers to binary (five binary places)  b.67.50

Answer 1

To convert the decimal number 67.50 to binary with five binary places, we need to convert both the integer part (67) and the fractional part (0.50) separately.

### Step 1: Convert the Integer Part (67)

1. Divide the integer by 2 and record the remainder.
2. Continue dividing the quotient by 2 until it becomes 0.

```
67 ÷ 2 = 33, remainder = 1
33 ÷ 2 = 16, remainder = 1
16 ÷ 2 = 8, remainder = 0
8 ÷ 2 = 4, remainder = 0
4 ÷ 2 = 2, remainder = 0
2 ÷ 2 = 1, remainder = 0
1 ÷ 2 = 0, remainder = 1
```

Now, reading the remainders from bottom to top, we get:

**67 in binary is 1000011.**

### Step 2: Convert the Fractional Part (0.50)

1. Multiply the fractional part by 2.
2. The whole number part of the result is the next binary digit.
3. Repeat with the new fractional part until you reach 5 binary places.

```
0.50 × 2 = 1.00 (whole number: 1, fractional part: 0.00)
0.00 × 2 = 0.00 (whole number: 0, fractional part: 0.00)
```

Since we only need 5 binary places and we can stop here because the fractional portion has reached 0:

**0.50 in binary is .1.**

### Combining Both Parts

Now, combine the integer and fractional parts:

**67.50 in binary (to five binary places) is:**

**1000011.1**

To express the fractional part in precisely five binary places, we can add four zeros as needed after the ".1":

**Final Answer: 1000011.10000**

This represents 67.50 in binary with five binary places after the decimal.