1/2  → 0  Remainder 1 (MSD)

The binary number is 11100₂.

Example 1.4

Convert decimal number 65₁₀ into binary.

Solution 1.4

Divide the number into 2 repeatedly and take the remainders:

65/2 → 32 Remainder 1 (LSD)

32/2 → 16 Remainder 0

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 (MSD)

The binary number is 1000001₂.

Example 1.5

Convert decimal number 122₁₀ into binary.

Solution 1.5

Divide the number into 2 repeatedly and take the remainders:

122/2 → 61 Remainder 0 (LSD)

61/2  → 30 Remainder 1

30/2  → 15 Remainder 0

15/2  → 7  Remainder 1

7/2   → 3  Remainder 1

3/2   → 1  Remainder 1

1/2   → 0  Remainder 1 (MSD)

The binary number is 1111010₂.

1.8 Converting Binary Numbers into Hexadecimal

To convert a binary number into hexadecimal, arrange the number in groups of four and find the hexadecimal equivalent of each group. If the number cannot be divided exactly into groups of four, insert zeros to the left of the number as needed so the number of digits are divisible by four.

Example 1.6

Convert binary number 10011111₂ into hexadecimal.

Solution 1.6

First, divide the number into groups of four, then find the hexadecimal equivalent of each group:

10011111 = 1001 1111

             9    F

The hexadecimal number is 9F₁₆.