Convert the following binary numbers to a decimal number. Show all steps

Question

a. (0101)2
b. (1001001)2
c. (11111100)2
d. (01011100)2
e. (11100100)2
f. (00000101)2
g. (11111100)2
h. (01001001)2
i. Take your own, at least 4 different binary number and convert it to
decimal.

Answer 1

a. (0101)2 = (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 4 + 0 + 1
= 5

b. (1001001)2 = (1 * 2^6) + (0 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 64 + 0 + 0 + 8 + 0 + 0 + 1
= 73

c. (11111100)2 = (1 * 2^7) + (1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 128 + 64 + 32 + 16 + 8 + 4 + 0 + 0
= 252

d. (01011100)2 = (0 * 2^7) + (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 0 + 64 + 0 + 16 + 8 + 4 + 0 + 0
= 92

e. (11100100)2 = (1 * 2^7) + (1 * 2^6) + (1 * 2^5) + (0 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 128 + 64 + 32 + 0 + 0 + 4 + 0 + 0
= 228

f. (00000101)2 = (0 * 2^7) + (0 * 2^6) + (0 * 2^5) + (0 * 2^4) + (0 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 0 + 0 + 0 + 0 + 0 + 4 + 0 + 1
= 5

g. (11111100)2 = (1 * 2^7) + (1 * 2^6) + (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 128 + 64 + 32 + 16 + 8 + 4 + 0 + 0
= 252

h. (01001001)2 = (0 * 2^7) + (1 * 2^6) + (0 * 2^5) + (0 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 0 + 64 + 0 + 0 + 8 + 0 + 0 + 1
= 73

i. (0110)2 = (0 * 2^3) + (1 * 2^2) + (1 * 2^1) + (0 * 2^0)
= 0 + 4 + 2 + 0
= 6

(010010)2 = (0 * 2^5) + (1 * 2^4) + (0 * 2^3) + (0 * 2^2) + (1 * 2^1) + (0 * 2^0)
= 0 + 16 + 0 + 0 + 2 + 0
= 18

(1011101)2 = (1 * 2^6) + (0 * 2^5) + (1 * 2^4) + (1 * 2^3) + (1 * 2^2) + (0 * 2^1) + (1 * 2^0)
= 64 + 0 + 16 + 8 + 4 + 0 + 1
= 93

(111000)2 = (1 * 2^5) + (1 * 2^4) + (1 * 2^3) + (0 * 2^2) + (0 * 2^1) + (0 * 2^0)
= 32 + 16 + 8 + 0 + 0 + 0
= 56