Converting Decimal to Binary or vice versa

We know that:

   2^0=1

   2^1=2

   2^2=4

   2^3=8

   2^4=16

   2^5=32

   2^6=64

   2^7=128

and so on. To convert the decimal number 75 to binary, we would find the largest power of 2 less than 75, which is 64. Thus, we would put a 1 in the 2^6 column, and subtract 64 from 75, giving us 11. The largest power of 2 in 11 is 8, or 2^3. Put 1 in the 2^3 column, and 0 in 2^4 and 2^5. Subtract 8 from 11 to get 3. Put 1 in the 2^1 column, 0 in 2^2, and subtract 2 from 3. We're left with 1, which goes in 2^0, and we subtract one to get zero. Thus, our number is 1001011.

 

Try converting these numbers from binary to decimal:

• 10
• 111
• 10101
• 11110

Remember:

      2^4| 2^3| 2^2| 2^1| 2^0

         |    |    |  1  |  0

         |    | 1  |  1  |  1

      1  | 0  | 1  |  0  |  1

      1  | 1  | 1  |  1  |  0

 

Converting Decimal to Hex and vice versa
Review the following tutorial on-line: http://www.math.ohiou.edu/~just/hex.htm
To convert from Hex to Binary:  http://www.permadi.com/tutorial/numDecToHex/

Basic Operations with HEX Numbers

To add two hex numbers

1. convert each number to binary

Hex to Binary
Hex value 6Ch, binary value = 0110 + 1100 = 01101100

2) use binary addition procedure

The addition process for multiple-bit binary numbers:

         1010

        +1111

       ______

• Step one:
  Column 2^0: 0+1=1.
  Record the 1.
  Temporary Result: 1; Carry: 0
• Step two:
  Column 2^1: 1+1=10.
  Record the 0, carry the 1.
  Temporary Result: 01; Carry: 1
• Step three:
  Column 2^2: 1+0=1 Add 1 from carry: 1+1=10.
  Record the 0, carry the 1.
  Temporary Result: 001; Carry: 1
• Step four:
  Column 2^3: 1+1=10. Add 1 from carry: 10+1=11.
  Record the 11.
  Final result: 11001

Alternately:

    11   (carry)

    1010

   +1111

  ______

   11001

3) convert result back to hex

To subtract two hex numbers

1) convert each number to binary

2) use binary subtraction procedure

3) convert result back to hex

 We can also do addition in hex itself. This addition is the

same as decimal addition EXCEPT we use a sixteen by sixteen

addition table instead of a ten by 10 addition table, and we

carry (or borrow) sixteen's not ten's.

Hex to Decimal
Hex value 6Ch, decimal value = 6*16 + C*1 = 6*16 + 12*1 = 108

Answers to Binary Problems:

 

Try converting these numbers from binary to decimal:

10=(1*2^1) + (0*2^0) = 2+0 = 2

111 = (1*2^2) + (1*2^1) + (1*2^0) = 4+2+1=7

10101= (1*2^4) + (0*2^3) + (1*2^2) + (0*2^1) + (1*2^0)=16+0+4+0+1=21

11110= (1*2^4) + (1*2^3) + (1*2^2) + (1*2^1) + (0*2^0)=16+8+4+2+0=30

 

 

       111      101      111

      +110     +111     +111

    ______    _____    _____

 

 

 

Ans1:                    1             1

          111            111            111

         +110           +110           +110

        ______         ______         _____

            1             01           1101

Ans2

 

          1                    1             1 

         101                   101            101

        +111                  +111           +111

       _____                 ____           _____

           0                    00           1100

Ans3

             1                  1             1

            111                 111            111

           +111                +111            111

          _____                _____           _____

              0                  10            1110