Binary Arithmetic: Arithmetic Addition

BINARY ARITHMETIC:

Arithmetic Addition:

The addition of two numbers in the signed magnitude follows the rules of ordinary arithmetic. In the signs are the same, add the two magnitudes and give the sum the common sign. If the signs are different, subtract the smaller magnitude from the larger and give the result the sign of the larger magnitude.

Binary addition

Problem: 39

Add the binary number (1001 1000)₂ and (00110110)₂

Solution:

Problem: 40

Add the numbers using binary addition (36)₁₀ and (24)₁₀.

Solution:

(36)₁₀ ⇒ (100100)₂

(24)₁₀ => 11000

Problem: 41

Add the numbers using binary addition (28)₁₀ and (-15)₁₀

(28)₁₀ → (11100)₂

(15)₁₀ → (01111)₂

- (15)₁₀ => 1's complement of (01111)₂ = 10000

(Note if carry generated add that carry)

Ans => (1101)₂

Problem: 42

Add the number using binary addition (-29)₁₀ and (14)₁₀

(11101)₂

(1110)₂

If there is no carry complement the result.

(1111)₂

Problem: 43

Add the number using binary addition (-28)₁₀ and (-14)₁₀.

(28)₁₀ ⇒ (011110)

(-28) ⇒ 1's complement of (-28)₁₀⇒ (100011)₂

(14)₁₀ ⇒ (0 1 1 1 0) ⇒ 1's complement of (-14)₁₀ ⇒ (1 0 0 0 1)₂