Advanced PIC Microcontroller Projects in C

Divide the number into 2 repeatedly and take the remainders:

28/2 → 14 Remainder 0 (LSD)

14/2 → 7  Remainder 0

7/2  → 3  Remainder 1

3/2  → 1  Remainder 1

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.

Example 1.7

Convert binary number 1110111100001110₂ into hexadecimal.

Solution 1.7

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

1110111100001110 = 1110 1111 0000 1110

                     E    F    0    E

The hexadecimal number is EF0E₁₆.

Example 1.8

Convert binary number 111110₂ into hexadecimal.

Solution 1.8

Since the number cannot be divided exactly into groups of four, we have to insert, in this case, two zeros to the left of the number so the number of digits is divisible by four:

111110 = 0011 1110

           3    E

The hexadecimal number is 3E₁₆.

Table 1.2 shows the hexadecimal equivalent of numbers 0 to 31.

Table 1.2: Hexadecimal equivalent of decimal numbers

Decimal	Hexadecimal	Decimal	Hexadecimal
0	0	16	10
1	1	17	11
2	2	18	12
3	3	19	13
4	4	20	14
5	5	21	15
6	6	22	16
7	7	23	17
8	8	24	18
9	9	25	19
10	A	26	1A
11	B	27	1B
12	C	28	1C
13	D	29	1D
14	E	30	1E
15	F	31	1F

1.9 Converting Hexadecimal Numbers into Binary

To convert a hexadecimal number into binary, write the 4-bit binary equivalent of each hexadecimal digit.

Example 1.9

Convert hexadecimal number A9₁₆ into binary.

Solution 1.9

Writing the binary equivalent of each hexadecimal digit:

A = 10102 9 = 10012

The binary number is 10101001₂.

Example 1.10

Convert hexadecimal number FE3C₁₆ into binary.

Solution 1.10

Writing the binary equivalent of each hexadecimal digit:

F = 11112 E = 11102 3 = 00112 C = 11002

The binary number is 1111111000111100₂.

1.10 Converting Hexadecimal Numbers into Decimal