AE 0601: Binary Operations
Digit
A symbol that is used to represent a single numerical quantity
2
Binary has a radix of
Negative numbers
Compliments are used to add
10
Decimal has a radix of
16
Hexadecimal has a radix of
Break down to sets of 4 digits and convert
How to convert binary to hexadecimal
Convert each digit into 4 digits
How to convert hexadecimal into binary
16
Increasing the fifth position by one in a binary system increases the number by
1
Increasing the first position by one in any number system increases the number by
8
Increasing the fourth position by one in a binary system increases the number by
1000
Increasing the fourth position by one in a decimal system increases the number by
4096
Increasing the fourth position by one in a hexadecimal system increases the number by
2
Increasing the second position by one in a binary system increases the number by
10
Increasing the second position by one in a decimal system increases the number by
16
Increasing the second position by one in a hexadecimal system increases the number by
4
Increasing the third position by one in a binary system increases the number by
100
Increasing the third position by one in a decimal system increases the number by
256
Increasing the third position by one in a hexadecimal system increases the number by
Positional notation
Method to convert binary or hexadecimal to decimal
Repeated multiplication method
Method used to convert the fractional portion of a decimal number to a hex or binary number
Repeated division method
Method used to convert the integer portion of a decimal number to a hex or binary number
Number system subscript
Small number to the right that denotes what number system is used (omitted in decimal system)
Radix
The base of a number system or the number of different symbols that may be used in any digit position
Most Significant Digit (MSD)
The digit of a number with the highest value due to its relative position
Least Significant Digit (LSD)
The digit of a number with the lowest value due to its relative position
Modulus
The number of combinations of a fixed number of digits
Digit position
The relative position of a digit in a number position that determines its relative value
Positional notation
The value of each digit position in a number system
Toggle 1's and 0's
To convert to 1's compliment
Toggle 1's and 0's then add 1
To convert to 2's compliment
Add any "carry over" past the MSD to the LSD
When adding using 1's compliment
Dismiss any "carry over" past the MSD
When adding using 2's compliment
MSD
When using the repeated division by 2 method, the final remainder is the
LSD
When using the repeated division by 2 method, the first remainder is the
