03a number systems
DESCRIPTION
Number systemsTRANSCRIPT
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