The document discusses binary arithmetic operations including addition, subtraction, and signed number arithmetic. It provides examples of adding 4-bit binary numbers in columns, demonstrating how to handle carries, as well as examples of adding and subtracting signed 2's complement numbers. The key steps for subtraction are outlined as appending leading zeros, taking the two's complement of the second term, adding the complemented number to the first term, and removing the most significant digit from the sum.

1. R.D.SIVAKUMAR, M.Sc., M.Phil., M.Tech.,
Assistant Professor of Computer Science &
Assistant Professor and Head, Department of M.Com.(CA),
Ayya Nadar Janaki Ammal College,
Sivakasi – 626 124.
Mobile: 099440-42243
e-mail : sivamsccsit@gmail.com
website: www.rdsivakumar.blogspot.in
BINARYARITHMETIC

2. Let's add 1101 to 1101 (assume both are 4-bit UB numbers).
Let the rightmost column be column 0, and the leftmost column be column 3.
First, add the right most column (column 0). Summing 1 + 1 results in 0, with a carry of 1 to
column 1.
Then, add the two bits in column 1, plus the carry bit. Summing 0 + 0, plus the carry 1, results
in 1, with a carry of 0 to column 2.
Then, add the two bits in column 2, plus the carry bit. Summing 1 + 1, plus the carry 0, results
in 0, with a carry of 1 to column 3.
Finally, add the two bits in column 3, plus the carry bit. Summing 1 + 1, plus the carry 1, results
in 1, with a carry of 1 to column 4. We've had to "create" a column 4 to place the fifth bit of the
sum.
An Example
ADDITION – UNSIGNED NUMBERS

3. BINARY ARITHMETIC –ADDITION – SIGNED NUMBERS
An Example
Adding signed numbers is not significantly different from adding unsigned numbers.
Recall that signed 4 bit numbers (2's complement) can represent numbers between -8
and 7. To see how this addition works, consider two examples.
Decimal Signed Binary
1110 (carry)
-2 1110
+3 0011
1 0001
Decimal Signed Binary
001 (carry)
-5 1011
+3 0011
-2 1110

4. BINARY ARITHMETIC – SUBTRACTION
An Example
Append leading zeros if necessary to represent both numbers with the same
number of digits. For example, convert 101-11 to 101-011 so that both have three
digits.
Apply two's complement to the second term : For each digit in the number,
change every 1 to 0 and every 0 to 1.
Add 1 to the number.
Add the complemented number to the first term. Now the original 101 -
11 has become 101 + 101 = 1010.
The sum in the previous step should have one more digit than you
started with. Remove the most significant digit from the sum to get 101 -
11 = 010. If you don't have an extra digit, you tried to subtract a larger
number from a smaller one.