06-10-2012, 04:49 PM
NUMBER SYSTEMS
NUMBER SYSTEMS.ppt (Size: 1.16 MB / Downloads: 55)
OBJECTIVES:
Discuss binary, octal and hexadecimal number.
Convert from decimal to binary, octal and hexadecimal and vice versa.
Determine the 1’s and 2’s complement of binary number.
Determine the signed number.
Arithmetic operations with binary, octal, hexadecimal and signed number.
Interpret the BCD Code and ASCII Code.
DECIMAL NUMBER
Base-ten system.
Decimal numbers use ten digits (0,1,2,3,4,5,6,7,8,9)
Table 1 shows the weighting for the decimal number up to 3 decimal places and 2 decimal places after the decimal point (.).
BINARY NUMBER
Base-two system.
Binary numbers use two digits (0,1).
Table 2 shows the weighting for the binary number up to 3 decimal places and 2 decimal places after the binary point (.).
The least significant bit (LSB) is the rightmost binary digit which has lowest weight of a given number.
The most significant bit (MSB) is the leftmost binary digit which has highest binary weight of a given number.
Converting decimal to binary
To convert decimal to binary use this approach:
i) Divide the decimal value by two and record
the remainder.
ii) Repeat step (i) until the decimal value is
equal to zero.
iii) The first remainder produced is the LSB in
the binary number and the last remainder is
the MSB.
Subtracting using 1’s Complement
For subtracting a smaller number from a larger
number, the 1’s complement method is as follows:
1. Determine the 1’s complement of the
smaller number.
2. Add the 1’s complement to the larger
number.
3. Remove the final carry and add it to the
LSB column. This step is called end-round
carry.