Part 3/8:

Most calculators and computers operate internally in base 10, making conversions from other bases to decimal essential.

Example: Converting Binary '111' to Decimal

• Step 1: Recognize '111' in binary represents (1 \times 2^2 + 1 \times 2^1 + 1 \times 2^0).

• Step 2: Replace the transition number '10' (which represents 2 in decimal) with 2.

• Step 3: Calculate: ((2^2) + (2^1) + (2^0) = 4 + 2 + 1 = 7).

Thus, binary '111' equals decimal 7.

Converting Between Other Bases

Example: Converting Base 4 '111' to Decimal

• Recognize that '111' in base 4 translates to (1 \times 4^2 + 1 \times 4^1 + 1 \times 4^0).

• Replace '10' with 4.

• Compute: (16 + 4 + 1 = 21).

Therefore, base 4 '111' equals decimal 21.