1.2 Number system_2021

1.2 Number system and Representation

Example 1 Hexadecimal to decimal conversion

Convert the hexadecimal number AFB216 to decimal number

Place Value 4096 256 16 1

Hexadecimal A (10) F (15) B (11) 2

Conversion 4096 x 10 256 x 15 16 x 11 1x2

Decimal 40960 + 3840 + 176 + 2 = 4497810

Hence, AFB216 = 4497810

1.2 Number system and Representation

Hexadecimal to decimal conversion

Example 2

Convert the hexadecimal number BA816 to decimal number

Place Value 4096 256 16 1

Hexadecimal B (11) A (10) 8

Conversion 256 x 11 16 x 10 1x8

Decimal 2816 + 160 + 8 = 298410

1.2 Number system and Representation

Example 3 Hexadecimal to decimal conversion

Convert the hexadecimal number AFFA16 to decimal number

Place Value 4096 256 16 1

Hexadecimal A (10) F (15) F (15) A (10)

Conversion 4096 x 10 256 x 15 16 x 15 1 x 10

Decimal 40960 + 3840 + 240 + 10 = 4505010

Hence, AFFA16 = 4505010

1.2 Number system and Representation

Hexadecimal to Binary
Conversion

1.2 Number System and Representation

Example 1 Hexadecimal to Binary

Convert the hexadecimal number 1A216 to binary number

Place Value 23 22 21 20 23 22 21 20 23 22 21 20
842184218421

Hexadecimal 1 A (10) 2

Binary 000110100010

Hence, 3FD16 = 1101000102

1.2 Number System and Representation

Example 2 Hexadecimal to Binary

Convert the hexadecimal number AF116 to binary number

Place Value 23 22 21 20 23 22 21 20 23 22 21 20
842184218421

Hexadecimal A (10) F (15) 1

Binary 101011110001

Hence, AF116 = 1010111100012

1.2 Number system and Representation

Binary to Hexadecimal
Conversion

1.2 Number system and Representation Binary to hexadecimal

Example 1

Convert the binary number 110102 to hexadecimal number

Place Value 23 22 21 20 23 22 21 20
84218421
Binary 00011010
Hexadecimal
1 8 + 2 = 10 (A)

Hence, 110102 = 1A16

1.2 Number system and Representation Binary to hexadecimal

Example 2

Convert the binary number 100102 to hexadecimal number

Place Value 23 22 21 20 23 22 21 20
84218421
Binary 00010010
Hexadecimal
12

Hence, 10010 2= 1216

1.2 Number system and Representation Binary to hexadecimal

Example 3

Convert the binary number 1111 to hexadecimal.

Solution:

Place Value 23 22 21 20 23 22 21 20
84218421

Binary 00001111

Hexadecimal 15 ( F)

Hence, 11112= F16

1.2 Number System and Representation

❑ Convert 45010 to binary number.
❑ Convert 1010102 to decimal number.
❑ Convert 3510 to hexadecimal number.

❑ Convert 45916 to decimal number.

❑ Convert 11010112 to hexadecimal number.
❑ Convert 7616 to binary number.

©Computer science unit KMPP 2019