Question

ve the following.
Convert (10111.011), into its decimal equivalent
Subtract (1101), from (100110).
Add the following binary numbers.
a. (1000), and (101)
b. (1011), and (10
d. (1111), and (1111) e. (11001), and (1
Convert the following decimal numbers into binary.
C. (128)10
a. (39)10
d. (55)10
b. (72)10
e. (173)10​

Answer 1

Answer:

Hexadecimal Numbers is a more complex system than using just binary or decimal and is mainly used when dealing with computers and memory address locations. By dividing a binary number up into groups of 4 bits, each group or set of 4 digits can now have a possible value of between “0000” (0) and “1111” ( 8+4+2+1 = 15 ) giving a total of 16 different number combinations from 0 to 15. Don’t forget that “0” is also a valid digit.

We remember from our first tutorial about Binary Numbers that a 4-bit group of digits is called a “nibble”. As 4-bits are also required to produce a hexadecimal number, a hex digit can also be thought of as a nibble, or half-a-byte. Thus two hexadecimal numbers are required to produce one full-byte ranging from 00 to FF.

Also, since 16 in the decimal system is the fourth power of 2 ( or 24 ), there is a direct relationship between the numbers 2 and 16 so one hex digit has a value equal to four binary digits so now q is equal to “16”.

Because of this relationship, four digits in a binary number can be represented with a single hexadecimal digit. This makes conversion between binary and hexadecimal numbers very easy, and hexadecimal can be used to write large binary numbers with much fewer digits.

The numbers 0 to 9 are still used as in the original decimal system, but the numbers from 10 to 15 are now represented by capital letters of the alphabet from A to F inclusive and the relationship between decimal, binary and hexadecimal is given below.