Question

What is the decimal representation of the following signed binary numbers?

Answer 1

Answer:

(10000000)₂ = -128 in decimal

(11001100)₂ = -52 in decimal

(10110111)₂ = -73 in decimal

Explanation:

NOTE: If Most Significant Bit is 0, it is positive number and if MSB is 1, it is negative number. If number is positive we can simply convert it to decimal. But if number is negative, follow following formula:

• (complement of the number) +1

EXAMPLE 1

  (10000000)₂

  (01 1 1 1 1 1 1)₂   ↔  complement of the number

+                    1

  (10000000)₂ = 1 ×$2^{7}$= 128 (magnitude in decimal)

But we remember MSB was 1 so answer is -128.

EXAMPLE 2

  (1 1 0 0 1 1 00)₂

  (0 0 1 1 0 0 1 1)₂

+                       1  

  (0 0 1 1 0 1 0 0)₂ = 52 (magnitude in decimal)

But we remember MSB was 1 so answer is -52.

EXAMPLE 3

  (1 0 1 1 0 1 1 1)₂

  (0 1 00 1 000)₂

+                      1  

  (01 00 1 00 1‬)₂ = 73 (magnitude in decimal)

But we remember MSB was 1 so answer is -73.