Arithmetic operations form the backbone of digital electronics, enabling the manipulation of Binary, Hexadecimal, and Binary Coded Decimal (BCD) numbers. Let's explore how these operations work in each number system.

**Binary Arithmetic Operations:**

In digital electronics, binary arithmetic involves addition, subtraction, multiplication, and division using binary numbers (base-2). Here's a brief overview:

**1) Binary Addition:**

0 + 0 = 0

0 + 1 = 1

1 + 0 = 1

1 + 1 = 10 (carry 1 to the next higher bit)

**Example:**

1101 (13 in decimal) + 1011 (11 in decimal) ______________ 11000 (24 in decimal, with a carry of 1)

**2) Binary Subtraction:**

0 - 0 = 0

1 - 0 = 1

1 - 1 = 0

If borrowing is required, borrow 1 from the next higher bit.

**Example:**

1101 (13 in decimal) - 1011 (11 in decimal) --> 010 (2 in decimal, with a borrow of 1)

**3) Binary Multiplication and Division:**

Similar to decimal multiplication and division, binary multiplication and division involve straightforward operations but require attention to detail.

**Hexadecimal Arithmetic Operations:**

Hexadecimal (base-16) is a convenient representation for binary-coded data, and arithmetic with hex numbers is more compact than binary. Hexadecimal uses the digits 0-9 and the letters A-F to represent values 0-15.

**1) Hexadecimal Addition:**

Addition in hexadecimal follows the same principles as binary, but the base is 16.

Carry values are 0 through 15.

**Example:**

9A (154 in decimal) + 27 (39 in decimal) ---> C1 (193 in decimal)

**2) Hexadecimal Subtraction:**

Similar to binary subtraction, but borrow values are 0 through 15.

**Example**:

B5 (181 in decimal) - 23 (35 in decimal) ---> 92 (146 in decimal)

__BCD Arithmetic Operations:____ __

BCD is a binary-coded representation of decimal numbers, where each decimal digit is represented by its 4-bit binary equivalent. BCD arithmetic operations are similar to binary arithmetic but with constraints to ensure that the result remains in BCD form.

**1) BCD Addition:**

If the sum of two BCD digits is greater than 9, a correction (add 6) is needed.

**Example:**

0101 (5 in decimal) + 0101 (5 in decimal) -->1010 (10 in decimal, corrected to BCD as 0000)

**2) BCD Subtraction:**

Like binary subtraction, but if borrowing is needed, subtract 6 from the borrowed value.

**Example:**

1001 (9 in decimal) - 0111 (7 in decimal) --> 010 (2 in decimal, corrected to BCD as 0010)

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