Question

Add and multiply the following numbers without converting to decimal(15F) and (A7)16

Answer 1

(15F)₁₆ + (A7)₁₆ =

Hexadecimal

0 1 2 3 4 5 6 7 8 9 A B C D E F  

F + 7  =  16        

Hence 1 will be carry over

5 + A + 1   =  10      

1 will be carry over

1 + 1 = 2

(15F)₁₆ + (A7)₁₆ = (206)₁₆

Converting into decimal

(15F)₁₆  = 1 x 16² + 5 x 16 + 15  = 256 + 80 + 15  = 351

(A7)₁₆  = 10 x 16  + 7  = 167

351 + 167 =   518

        518

16         32    6

16            2   0

16            0    2

518 =  (206)₁₆

(15F)₁₆ + (A7)₁₆ = (206)₁₆

There is a carry of 1 to the next higher order place when the sum of two digits is greater than the highest digit in the number system.

When the sum is more than 9, there is a carry in decimal.

When the total of two digits is more than F in hexadecimal, there is a carry.

At the unit's location, add

F + 7 = (F+1) + 6 = 10 + 6 = 16, or 6 with a carry of 1.

Adding at position 16 plus the carry of 1

The result (5+a)+1=F+1=10 is 0 with a carry of 1.

adding at the 162 position and carrying

1+0+1=2

The response is 206.

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