The last three digits of the binary equivalent of the number 85432578 is

Options

A. `001`
B. `100`
C. 110
D. `010`

Explanation

To find the last three digits of the binary equivalent of the number 85432578, we can follow these steps:

### Step 1: Divide the number by 2
We start by dividing the number by 2 and noting down the remainder. The remainder will tell us the last digit in binary.

**Calculation:**
- 85432578 ÷ 2 = 42716289 with a remainder of 0.

### Step 2: Continue dividing the quotient by 2
Next, we take the quotient from the previous division and divide it by 2 again, recording the remainder.

**Calculation:**
- 42716289 ÷ 2 = 21358144 with a remainder of 1.

### Step 3: Repeat the process
We continue this process until we have enough remainders to find the last three digits.

**Calculation:**
- 21358144 ÷ 2 = 10679072 with a remainder of 0.
- 10679072 ÷ 2 = 5339536 with a remainder of 0.
- 5339536 ÷ 2 = 2669768 with a remainder of 0.
- 2669768 ÷ 2 = 1334884 with a remainder of 0.
- 1334884 ÷ 2 = 667442 with a remainder of 0.
- 667442 ÷ 2 = 333721 with a remainder of 0.
- 333721 ÷ 2 = 166860 with a remainder of 1.
- 166860 ÷ 2 = 83430 with a remainder of 0.
- 83430 ÷ 2 = 41715 with a remainder of 0.
- 41715 ÷ 2 = 20857 with a remainder of 1.
- 20857 ÷ 2 = 10428 with a remainder of 1.
- 10428 ÷ 2 = 5214 with a remainder of 0.
- 5214 ÷ 2 = 2607 with a remainder of 0.
- 2607 ÷ 2 = 1303 with a remainder of 1.
- 1303 ÷ 2 = 651 with a remainder of 1.
- 651 ÷ 2 = 325 with a remainder of 1.
- 325 ÷ 2 = 162 with a remainder of 1.
- 162 ÷ 2 = 81 with a remainder of 0.
- 81 ÷ 2 = 40 with a remainder of 1.
- 40 ÷ 2 = 20 with a remainder of 0.
- 20 ÷ 2 = 10 with a remainder of 0.
- 10 ÷ 2 = 5 with a remainder of 0.
- 5 ÷ 2 = 2 with a remainder of 1.
- 2 ÷ 2 = 1 with a remainder of 0.
- 1 ÷ 2 = 0 with a remainder of 1.

### Step 4: Collect the remainders
Now we collect the remainders from the last division to the first. The last three remainders we collected are:

- 1 (from 1)
- 0 (from 2)
- 1 (from 5)

### Conclusion
Reading the last three remainders from bottom to top gives us the last three digits of the binary equivalent of 85432578, which is **001**.

### Final Answer
The last three digits of the binary equivalent of the number 85432578 is **001**.