Question

Convert the following Binary numbers into decimal numbers.
a) 11001
b) 111001
c) 100011
d) 100101
e) 110011
f) 101011​

Answer 1

Answer:

a) 11001

= (1×2⁴) + (1×2³) + (0×2²) + (0×2¹) + (1×2⁰)

= 16 + 8 + 0 + 0 + 1

= 25

Hence, (11001)₂ = (25)₁₀

b) 111001

= (1×2⁵) + (1×2⁴)+ (1×2³) + (0×2²) + (0×2¹) + (1×2⁰)

= 32 + 16 + 8 + 0 + 0 + 1

= 57

Hence, (111001)₂ = (57)₁₀

c) 100011

= (1×2⁵) + (0×2⁴) + (0×2³) + (0×2²) + (1×2¹) + (1×2⁰)

= 32 + 0 + 0 + 0 + 2 + 1

= 35

Hence, (100011)₂ = (35)₁₀

d) 100101

= (1×2⁵) + (0×2⁴) + (0×2³) + (1×2²) + (0×2¹) + (1×2⁰)

= 32 + 0 + 0 + 4 + 0 + 1

= 37

Hence, (100101)₂ = (37)₁₀

e) 110011

= (1×2⁵) + (1×2⁴) + (0×2³) + (0×2²) + (1×2¹) + (1×2⁰)

= 32 + 16 + 0 + 0 + 2 + 1

= 51

Hence, (110011)₂ = (51)₁₀

f) 101011

= (1×2⁵) + (0×2⁴) + (1×2³) + (0×2²) + (1×2¹) + (1×2⁰)

= 32 + 0 + 8 + 0 + 2 + 1

= 43

Hence, (101011)₂ = (43)₁₀

Explanation:

Here, we take the digits place value in numbers starting from 0 but the digits place value increases only 1 after every digit. Then, we will multiply each and every digits face value with 2 (including the power of their respective place value). After that, we will add the results to get the number in decimal number system.