Compute the following subtraction in hexadecimal form AABB

Compute the following subtraction in hexadecimal form: AABB - DCF. Represent the exercise and its solution in standard binary form. (b) Compute the following addition in 2s complement binary form with 6 bits: 110110 + 111010. Represent the exercise and its solution in decimal form.

Solution

1. (a) 1) In the hexadecimal system we borrow a group of 16₁₀. Thus the given problem is

AABB₁₆ - DCF₁₆ = 9CEC₁₆   16 borrow

AABB = 43707₁₀

- 0DCF = 3535₁₀

9CEC = 40172₁₀

2) Above numbers in standard binary form is obtained by replacing each hex bits by its equivalen 4 binary bits.

AABB₁₆ = 1010 1010 1011 1011₂

  0DCF₁₆  = 0000 1101 1100 1111₂

9CEC₁₆  = 1001 1100 1110 1100₂

(b) 1) 2s complement binary addition:

Since both are not negative integers, we don\'t have to use two\'s complement for addition.

110110₂ + 111010₂ = 1110000₂

2) Above exercise in decimal form is 54₁₀ + 58₁₀ = 112₁₀