Question :- what is the binary subtraction of 101001-010110? → 010011 (Ans.)

Procedures for Binary Subtraction by 1’s Complement

1. Write the 1’s complement of the subtrahend.
2. Then add the 1’s complement subtrahend with the minuend.
3. If the result has a carryover, then add that carry over in the least significant bit.

Binary Subtraction Using 1’s Complement

1. Step 1: Find the 1’s complement of the subtrahend, which means the second number of subtraction.
2. Step 2: Add it with the minuend or the first number.
3. Step 3: If there is a carryover left then add it with the result obtained from step 2.

To subtract a larger number from a smaller one, switch the order of the numbers, do the subtraction, then add a negative sign to the answer. For example, to solve the binary problem 11 – 100, solve for 100 – 11 instead, then add a negative sign to the answer.

100
4 in binary is 100. Unlike the decimal number system where we use the digits 0 to 9 to represent a number, in a binary system, we use only 2 digits that are 0 and 1 (bits). We have used 3 bits to represent 4 in binary.

As binary notation only has two digits, subtracting a “0” from a “0” or a “1” leaves the result unchanged as 0-0 = 0 and 1-0 = 1. Subtracting a “1” from a “1” results in a “0”, but subtracting a “1” from a “0” requires a borrow. In other words 0 – 1 requires a borrow.

So, the subtraction of two signed binary numbers is similar to the addition of two signed binary numbers. But, we have to take 2’s complement of the number, which is supposed to be subtracted. This is the advantage of 2’s complement technique. Follow, the same rules of addition of two signed binary numbers.

Binary subtraction is also similar to that of decimal subtraction with the difference that when 1 is subtracted from 0, it is necessary to borrow 1 from the next higher order bit and that bit is reduced by 1 (or 1 is added to the next bit of subtrahend) and the remainder is 1.

To convert integer to binary, start with the integer in question and divide it by 2 keeping notice of the quotient and the remainder. Continue dividing the quotient by 2 until you get a quotient of zero. Then just write out the remainders in the reverse order. Here is an example of such conversion using the integer 12.

10
Counting in binary

1011.011 from binary to decimal is 11.375.

Exercise :: Arithmetic Operations and Circuits – General Questions

4-bit binary Adder-Subtractor. Last Updated: 27-08-2019. In Digital Circuits, A Binary Adder-Subtractor is one which is capable of both addition and subtraction of binary numbers in one circuit itself. The operation being performed depends upon the binary value the control signal holds.

To subtract a larger number from a smaller one, switch the order of the numbers, do the subtraction, then add a negative sign to the answer. For example, to solve the binary problem 11 – 100, solve for 100 – 11 instead, then add a negative sign to the answer. (This rule applies to subtraction in any base, not just binary.) Thanks!

This suggests that when K=1, the operation being performed on the four bit numbers is subtraction. Similarly If the Value of K=0, B0 (exor) K=B0. The operation is A+B which is simple binary addition. This suggests that When K=0, the operation being performed on the four bit numbers is addition.

The circuit consists of 4 full adders since we are performing operation on 4-bit numbers. There is a control line K that holds a binary value of either 0 or 1 which determines that the operation being carried out is addition or subtraction.