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