NAND2TET UNIT 2 Binary Arithmetic

Question 1

In general, let x = x_nx_n-1 … x₀ be a string of digits. The value of x in base b, denoted (x)_b, is defined as follows…

Answer 1

(x_nx_n-1 … x₀)_b = Σx_{i *} bⁱ

Example:

(10011)₂ =1*2⁴ + 0*2³ ​+0*2² ​+1*2¹ ​+1*2⁰ ​

= 1*16 + 0*8 + 0*4 + 1*2 + 1*1

=19

Question 2

Answer 2

Binary addition