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Revision Exercise

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Revision Exercise

Hexadecimal Number System

Hexadecimal System

- 16 different values possible:
- 0 1 2 3 4 5 6 7 8 9 A B C D E F
(0 – 9) (10 11 12 13 14 15)

- A to F represent numbers 10 to 15

- 0 1 2 3 4 5 6 7 8 9 A B C D E F
- Base 16
- E.g. C416

Binary to Hexadecimal Conversion

Q: Convert 011011102 to hexadecimal.

A:

8

4

2

1

8

4

2

1

0

1

1

0

1

1

1

0

4 + 2

8 + 4 + 2

6

14 = E

6E16

Hexadecimal to Binary Conversion

Q: Convert C416 to binary.

A:

8

4

2

1

8

4

2

1

1

1

0

0

0

1

0

0

2

8 + 4

4

C = 12

C416

- Decimal to Hexadecimal Example 1

- Q: Convert 4110 to hex
A:

16

41

16

2

Remainder 9

0

Remainder 2

Ans: 4110 = 2916

- Decimal to Hexadecimal Example 2

- Q: Convert 10910 to hex
A:

16

109

16

6

Remainder 13

0

Remainder 6

Ans: 10910 = 6 1316

= 6 D16

- Hexadecimal to Decimal Example 1

- Q: Convert 3C16 to decimal
A:

161

160

- Step 1: Place Values

3

C

- Step 2: Multiply by place value

(3 x 16) + (C x 1)

- Step 3: Hex value for letters

(3 x 16) + (12 x 1)

- Step 4: Add values

48 + 12

6010

- Hexadecimal to Decimal Example 2

- Q: Convert 1F16 to decimal
A:

161

160

- Step 1: Place Values

1

F

- Step 2: Multiply by place value

(1 x 16) + (C x 1)

- Step 3: Hex value for letters

(1 x 16) + (15 x 1)

- Step 4: Add values

16 + 15

3110

- Decimal to Hexadecimal Short Method

Q: Convert 13910 to hexadecimal.

A:

- convert 13910 to binary
- 13910 100010112

- convert from 100010112 to hexadecimal.
- 100010112

8B16

- Hexadecimal to Decimal Short Method

Q: Convert 1F16 to decimal.

A:

- convert 1F16 to binary
- 1F16 000111112

- convert from 000111112 to decimal.
- 000111112

3110