Hexadecimal Numbers

Hexadecimal numbers are base 16.

There are 16 different hex digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c, d, e, or f

Hex Digit	0	1	2	3	4	5	6	7	8	9	a	b	c	d	e	f
Decimal Value	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15
Binary Value	0000	0001	0010	0011	0100	0101	0110	0111	1000	1001	1010	1011	1100	1101	1110	1111

Place Value Table

161	160
16	1

---

Example 1: Convert the hex number 5e to decimal.

Step 1: Multiply each hex digit by its place value.

Step 2: Add the resulting numbers.

16	1
5	e
5 × 16 = 80	14 × 1 = 15
80  +	15 =    95

---

Example 2: Convert the 4-bit binary number 1110 to hex.

Find the hex digit by looking it up in the table.

1110 = e

---

Example 3: Convert the 8-bit binary number 01101110 to hex.

Step 1: Separate the binary digits into groups of 4:	0110	1110
Step 2: Convert each group of digits to hex:	6	e

01101110 = 6e

---

Example 4: Convert the hex number 8f to binary.

Look up each hex digit in the table, and write its binary value.

hex 8 = 1000

hex f = 1111

Therefore, 8f = 10001111

---

We use hexadecimal to represent numbers because it is:
a) easy to convert hex to binary,
b) easy to convert binary to hex,
c) easier to read 2 digits than 8 digits.