What is the decimal representation of the following signed binary numbers?
1
11001100
10110111

(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:

EXAMPLE 1

  (10000000)₂

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

+                    1

  (10000000)₂ = 1 ×= 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.

answer; i believe the correct answer is 50 pounds;

ιт ιѕ ωнєи ѕσмєσиє ρυтѕ ιи α ¢σ∂є σя ѕσмєтнιиg тнαт вяιиgѕ α νιяυѕ, σя мєѕѕєѕ уσυя gαмє υρ, σя αℓℓσωѕ тнєм тσ ¢нєαт.

αи∂ уєѕ ι нανє вєєи нα¢кє∂ вєfσяє(ιт αιит fυи)

нσρє ι ¢συℓ∂ нєℓρ уσυ.