Hexadecimal Addition

HexadecimalAddition

Decimalbasic concepts:

Decimalis base 10.

Thereare 10 digits in counting (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)

Whenyou reach 10, you carry a “1” over to the next column

Thenumber after 9 is 10

Hexadecimalbasic concepts:

Hexadecimalis base 16.

Thereare 16 digits in counting (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D,E, F)

Whenyou reach 16, you carry a “1” over to the next column

Thenumber after F (decimal 15) is 10 in hex (or 16 in decimal)

Use thefollowing steps to perform hexadecimal addition:

1. Addone column at a time.

2. Convertto decimal and add the numbers.

3a. If the result of step two is 16 orlarger subtract the result from 16 and carry 1 to the next column.

3b. If the result of step two is lessthan 16, convert the number to hexadecimal.

Example: (Use the color code ineach step to see what’s happening)

The problem: You are to add these numbers:
		A	C	5	A	9
		E	D	6	9	4

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Carry Over:
1. Add one column at a time 2. Convert to decimal & add (9 + 4 = 13) 3. Follow less than 16 rule Decimal 13 is hexadecimal D		A	C	5	A	9
		E	D	6	9	4
						D

*********************************************************************************

Carry Over:				1
1. Add next column 2. Convert to decimal & add (10 + 9 = 19) 3. Follow 16 or larger than 16 rule (19 – 16 = 3 carry a 1)		A	C	5	A	9
		E	D	6	9	4
					3	D

*********************************************************************************

Carry Over:				1
1. Add next column 2. Convert to decimal & add (1 + 5 + 6 = 12) 3. Follow less than 16 rule, convert to hex Decimal 12 is hexadecimal C		A	C	5	A	9
		E	D	6	9	4
				C	3	D

*********************************************************************************

Carry Over:		1
1. Add next column 2. Convert to decimal & add (12 + 13 = 25) 3. Follow 16 or larger than 16 rule (25 – 16 = 9 carry a 1)		A	C	5	A	9
		E	D	6	9	4
			9	C	3	D

*********************************************************************************

Carry Over:		1
1. Add next column 2. Convert and add (1 + 10 + 11 = 22) 3. Follow 16 or larger than 16 rule (22 – 16 = 6 carry a 1)			A	C	5	A	9
			B	D	6	9	4
			6	9	C	3	D

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Carry Over:		1
1. Add next column 2. Convert and add (1 + 0 + 0 = 1) 3. Follow less than 16 rule		0	A	C	5	A	9
		0	B	D	6	9	4
		1	6	9	C	3	D

For substraction

http://www.wisc-online.com/objects/ViewObject.aspx?ID=TMH3703

complement the substraction portion and do normal addition as explained above

  569D
-  FDA

  569D
- 0FDA

Now find complement of 0FDA = convert every bit to dec and 16-val.
So, 0FDA becomes F025