Question

pseudo code c

• Explain how you add fixed-width digits in a decimal number system.
  • How do you do this in binary?
  • How do you do this in hexadecimal?
• Explain how you subtract numbers in digits in a decimal number system.
  • How do you do this in binary?
  • How do you do this in hexadecimal?

Answer 1

Example 63 (x)+ 89 (y) => 52 (sum) and carry=1

Add fixed-width decimal integers; N digits.

1:  carry ← 0 //initiliazzed caarry as 0
2:  for i = 0 to N // i-th bit
3:   sum_i ← (x_i + y_i + carry) % 10 // mod operation if we add 9+3 then sum(i) will be (9+3)%10=2
4:   carry ← (x_i + y_i + carry) ∕ 10 //div operation carry=(9+3)/10=1
5:  end for //end loop

Add fixed-width binary integers; N bits.

1:  carry ← 0
2:  for i = 0 to N // i-th bit
3:   sum_i ← (x_i + y_i + carry) % 2 // mod operation
4:   carry ← (x_i + y_i + carry) ∕ 2 // division operation
5:  end for

Add fixed-width integers in hexadecimal; N digits.

1:  carry ← 0
2:  for i = 0 to N − 1 // i-th digit
3:   sum_i ← (x_i + y_i + carry) % 16 //mod
4:   carry ← (x_i + y_i + carry) ∕ 16 //division
5:  end for

Subtract fixed-width decimal integers; N digits.

1:  borrow ← 0
2:  for i = 0 to N − 1 do // i-th digit
3:   if y_i ≤ x_i then //subtract Y from X
4:   difference_i ← (x_i − y_i)
5:   else if i = N − 1 then
6:   borrow ← 1 // Result will be wrong!
7:   x_i ← x_i + 10
8:   difference_i ← (x_i − y_i)
9:   else
10:   j ← i + 1
11:   while x_j = 0 do
12:   j ← j + 1
13:   end while
14:   x_j ← x_j − 1
15:   j ← j − 1
16:   while j > i do
17:   x_j ← x_j + 10 − 1
18:   j ← j − 1
19:   end while
20:   difference_i ← (10+ x_i − y_i)
21:   end if
22:  end for

Subtract fixed-width binary integers; N digits.

1:  borrow ← 0
2:  for i = 0 to N − 1 do // i-th digit
3:   if y_i ≤ x_i then //subtract Y from X
4:   difference_i ← (x_i − y_i)
5:   else if i = N − 1 then
6:   borrow ← 1 //Result will be wrong!
7:   x_i ← x_i + 2 // if we subtract 1 from 0 we cannot so we have to take borrow from left side now //will be 0+(2 if binary ,10 for decibal and 16 for hexadecimal)
8:   difference_i ← (x_i − y_i)
9:   else
10:   j ← i + 1
11:   while x_j = 0 do
12:   j ← j + 1
13:   end while
14:   x_j ← x_j − 1
15:   j ← j − 1
16:   while j > i do
17:   x_j ← x_j + 2− 1
18:   j ← j − 1
19:   end while
20:   difference_i ← (2+ x_i − y_i)
21:   end if
22:  end for

Subtract fixed-width hexadecimal integers; N digits.

1:  borrow ← 0
2:  for i = 0 to N − 1 // i-th digit
3:   if y_i ≤ x_i then //subtract Y from X
4:   difference_i ← (x_i − y_i)
5:   else if i = N − 1 then
6:   borrow ← 1 //Result will be wrong!
7:   x_i ← x_i + 16
8:   difference_i ← (x_i − y_i)
9:   else
10:   j ← i + 1
11:   while x_j = 0 do
12:   j ← j + 1
13:   end while
14:   x_j ← x_j − 1
15:   j ← j − 1
16:   while j > i do
17:   x_j ← x_j + 16 − 1
18:   j ← j − 1
19:   end while
20:   difference_i ← (16 + x_i − y_i)
21:   end if
22:  end for

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