Advanced PIC Microcontroller Projects in C

To convert a hexadecimal number into decimal, calculate the sum of the powers of 16 of the number.

Example 1.11

Convert hexadecimal number 2AC₁₆ into decimal.

Solution 1.11

Calculating the sum of the powers of 16 of the number:

2AC₁₆ = 2 × 16² + 10 × 16¹ + 12 × 16⁰

      = 512 + 160 + 12

      = 684

The required decimal number is 684₁₀.

Example 1.12

Convert hexadecimal number EE₁₆ into decimal.

Solution 1.12

Calculating the sum of the powers of 16 of the number:

EE₁₆ = 14 × 16¹ + 14 × 16⁰

     = 224 + 14

     = 238

The decimal number is 238₁₀.

1.11 Converting Decimal Numbers into Hexadecimal

To convert a decimal number into hexadecimal, divide the number repeatedly by 16 and take the remainders. The first remainder is the LSD, and the last remainder is the MSD.

Example 1.13

Convert decimal number 238₁₀ into hexadecimal.

Solution 1.13

Dividing the number repeatedly by 16:

238/16 → 14 Remainder 14 (E) (LSD)

14/16  → 0  Remainder 14 (E) (MSD)

The hexadecimal number is EE₁₆.

Example 1.14

Convert decimal number 684₁₀ into hexadecimal.

Solution 1.14

Dividing the number repeatedly by 16:

684/16 → 42 Remainder 12 (C) (LSD)

42/16  → 2  Remainder 10 (A)

2/16   → 0  Remainder 2      (MSD)

The hexadecimal number is 2AC₁₆.

1.12 Converting Octal Numbers into Decimal

To convert an octal number into decimal, calculate the sum of the powers of 8 of the number.

Example 1.15

Convert octal number 15₈ into decimal.

Solution 1.15

Calculating the sum of the powers of 8 of the number:

15₈ = 1 × 8¹ + 5 × 8⁰

     = 8 + 5

     = 13

The decimal number is 13₁₀.

Example 1.16

Convert octal number 237₈ into decimal.

Solution 1.16

Calculating the sum of the powers of 8 of the number:

237₈ = 2 × 8² + 3 × 8¹ + 7 × 8⁰

     = 128 + 24 + 7

     = 159

The decimal number is 159₁₀.

1.13 Converting Decimal Numbers into Octal

To convert a decimal number into octal, divide the number repeatedly by 8 and take the remainders. The first remainder is the LSD, and the last remainder is the MSD.

Example 1.17

Convert decimal number 159₁₀ into octal.

Solution 1.17

Dividing the number repeatedly by 8:

159/8 → 19 Remainder 7 (LSD)

19/8  → 2  Remainder 3

2/8   → 0  Remainder 2 (MSD)

The octal number is 237₈.

Example 1.18

Convert decimal number 460₁₀ into octal.

Solution 1.18

Dividing the number repeatedly by 8:

460/8 → 57 Remainder 4 (LSD)

57/8  → 7  Remainder 1

7/8   → 0  Remainder 7 (MSD)

The octal number is 714₈.

Table 1.3 shows the octal equivalent of decimal numbers 0 to 31.

Table 1.3: Octal equivalent of decimal numbers

Decimal	Octal	Decimal	Octal
0	0	16	20
1	1	17	21
2	2	18	22
3	3	19	23
4	4	20	24
5	5	21	25
6	6	22	26
7	7	23	27
8	10	24	30
9	11	25	31
10	12	26	32
11	13	27	33
12	14	28	34
13	15	29	35
14	16	30	36
15	17	31	37

1.14 Converting Octal Numbers into Binary

To convert an octal number into binary, write the 3-bit binary equivalent of each octal digit.

Example 1.19