DECIMAL BINARY

a) 20310

b) 010011102

c)

d) 110100002

e)

f) 7510

Revision ExerciseDECIMAL BINARY

a) 20310 110010112

b) 7810 010011102

c) 24910 111110012

d) 20810 110100002

e) 17110 101010112

f) 7510 010010112

Hexadecimal Number 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

–Base 16

– E.g. C416

Hexadecimal System

Binary to Hexadecimal Conversion

Q: Convert 011011102 to hexadecimal.

A:2 1482 148

1 0110110

4 + 2 8 + 4 + 2

6 14 = E 6E16

Hexadecimal to Binary Conversion

Q: Convert C416 to binary.

A:2 1482 148

0 0100011

8 + 4

C = 12 4 C416

2

Decimal to Hexadecimal Example 1

Ans: 4110 = 2916

Q: Convert 4110 to hex

A: 4116

2 Remainder 916

0 Remainder 2

Decimal to Hexadecimal Example 2

Ans: 10910 = 6 1316

Q: Convert 10910 to hex

A: 10916

6 Remainder 1316

0 Remainder 6

= 6 D16

Hexadecimal to Decimal Example 1

Q: Convert 3C16 to decimal

A:

160161

Step 1: Place Values

Step 2: Multiply by place value

Step 3: Hex value for letters

48 + 12

3 C

(3 x 16) + (C x 1)

(3 x 16) + (12 x 1)

Step 4: Add values

6010

Hexadecimal to Decimal Example 2

Q: Convert 1F16 to decimal

A:

160161

Step 1: Place Values

Step 2: Multiply by place value

Step 3: Hex value for letters

16 + 15

1 F

(1 x 16) + (C x 1)

(1 x 16) + (15 x 1)

Step 4: Add values

3110

Q: Convert 13910 to hexadecimal.

A:1) convert 13910 to binary

– 13910 100010112

2) convert from 100010112 to hexadecimal.– 100010112 8B16

Decimal to Hexadecimal Short Method

Hexadecimal to Decimal Short Method

Q: Convert 1F16 to decimal.

A:1) convert 1F16 to binary

– 1F16 000111112

2) convert from 000111112 to decimal.– 000111112 3110