03a number systems

Second Semester 2014-2015

Number Systems

Decimal Number System

Base 1010 possible

values

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Binary Number System

Base 22 possible

values

0 and 1

Octal Number System

Base 88 possible

values

0, 1, 2, 3, 4, 5, 6, 7

Hexadecimal Number System

Base 1616 possible

values

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F

Number System Conversion

Decimal to other number systems (whole number)

Write the remainders in reverse order

Do this until the quotient becomes 0

Obtain the remainder

Divide the decimal number by the base

Decimal to other number systems (whole number)

• Convert 2410 to binary, octal and hexadecimal

24/2 = 12 r. 0

Decimal to other number systems (whole number)

• Convert 2410 to binary, octal and hexadecimal

24/2 = 12 r. 0

12/2 = 6 r. 0

Decimal to other number systems (whole number)

• Convert 2410 to binary, octal and hexadecimal

24/2 = 12 r. 0

12/2 = 6 r. 0

6/2 = 3 r. 0

Decimal to other number systems (whole number)

• Convert 2410 to binary, octal and hexadecimal

24/2 = 12 r. 0

12/2 = 6 r. 0

6/2 = 3 r. 0

3/2 = 1 r. 1

Decimal to other number systems (whole number)

• Convert 2410 to binary, octal and hexadecimal

24/2 = 12 r. 0

12/2 = 6 r. 0

6/2 = 3 r. 0

3/2 = 1 r. 1

1/2 = 0 r. 1

Decimal to other number systems (whole number)

• Convert 2410 to binary, octal and hexadecimal

24/2 = 12 r. 0 2410 = 110002

12/2 = 6 r. 0

6/2 = 3 r. 0

3/2 = 1 r. 1

1/2 = 0 r. 1

Decimal to other number systems (fraction part)

Write the obtained whole number

Do this until the product becomes a whole number

Take note of the whole number

Multiply the fractional part by the base

Decimal to other number systems (fraction part)

• Convert 24.75 to binary, octal, and hexadecimal

0.75 x 2 = 1.50

Decimal to other number systems (fraction part)

• Convert 24.75 to binary, octal, and hexadecimal

0.75 x 2 = 1.50

0.50 x 2 = 1.0

Decimal to other number systems (fraction part)

• Convert 24.75 to binary, octal, and hexadecimal

0.75 x 2 = 1.50 24.7510 = 11000.112

0.50 x 2 = 1.0

Binary, Octal, Hexadecimal to Decimal

Convert the number in positional form and evaluate to

obtain its decimal equivalent.

Binary, Octal, Hexadecimal to Decimal

• Convert 11000.112 to decimal.

1 1 0 0 00 x 20 = 0

Binary, Octal, Hexadecimal to Decimal

• Convert 11000.112 to decimal.

1 1 0 0 00 x 20 = 00 x 21 = 0

Binary, Octal, Hexadecimal to Decimal

• Convert 11000.112 to decimal.

1 1 0 0 00 x 20 = 00 x 21 = 00 x 22 = 0

Binary, Octal, Hexadecimal to Decimal

• Convert 11000.112 to decimal.

1 1 0 0 00 x 20 = 00 x 21 = 00 x 22 = 01 x 23 = 8

Binary, Octal, Hexadecimal to Decimal

• Convert 11000.112 to decimal.

1 1 0 0 00 x 20 = 00 x 21 = 00 x 22 = 01 x 23 = 81 x 24 = 16

24

Binary, Octal, Hexadecimal to Decimal

• Convert 11000.112 to decimal.

. 1 1

1 x 2-1 = 0.51 x 2-2 = 0.25

0.75

11000.112 = 25.7510

Binary to Octal

Convert each 3 digit binary number into its Decimal equivalent.

Pad in 0’s to fill the 3 slots in a group.

Moving from the radix point outward, group the binary digits in 3’s.

Binary to Octal

• Convert 1001011.11 to binary

1001011.110

6 in decimal

Binary to Octal

• Convert 1001011.11 to binary

1001011.110

3 in decimal

Binary to Octal

• Convert 1001011.11 to binary

1001011.110

1 in decimal

Binary to Octal

• Convert 1001011.11 to binary

001001011.110

1 in decimal

Binary to Octal

• Convert 1001011.11 to binary

001001011.110

1001011.112 = 113.68

Binary to Hexadecimal

Convert each 3 digit binary number into its Decimal equivalent.

Pad in 0’s to fill the 4 slots in a group.

Moving from the radix point outward, group the binary digits in 4’s.

Octal to Binary

Convert each octal digit to it’s 3-digit binary equivalent

Hexadecimal to Binary

Convert each octal digit to it’s 4-digit binary equivalent