Question

binary to decimal conversion
use the table to convert these binary numbers to decimal numbers. show your work by filling in each table.

1. convert 101 to a decimal number using the table. 5

powers of 2 2^7 2^6 2^5 2^4 2^3 2^2 2^1 2^0
equivalent 128 64 32 16 8 4 2 1
binary = 101
decimal =

1. convert 100 to a decimal number using the table. 4

Explanation:

Step1: Analyze binary digits for 101

For binary number 101, from right - most digit:
The right - most digit (corresponding to $2^0$) is 1, the middle digit (corresponding to $2^1$) is 0, and the left - most digit (corresponding to $2^2$) is 1.

Step2: Calculate decimal value for 101

\[1\times2^2+0\times2^1 + 1\times2^0=4 + 0+1=5\]

Step3: Analyze binary digits for 100

For binary number 100, from right - most digit:
The right - most digit (corresponding to $2^0$) is 0, the middle digit (corresponding to $2^1$) is 0, and the left - most digit (corresponding to $2^2$) is 1.

Step4: Calculate decimal value for 100

\[1\times2^2+0\times2^1+0\times2^0 = 4+0 + 0=4\]

Answer:

1. Decimal value of 101 is 5
2. Decimal value of 100 is 4