Binary Problem Convert the binary number 1011 to

Binary

Problem Convert the binary number 1011 to a decimal number. Write the binary number on paper 8 4 2 1 x x 1 0 1 1 8 + 0 +2 + 1 = 11

Problem Convert the binary number 101011 to a decimal number. Write the binary number on paper 32 x 1 8 4 2 1 0 1 1 16 x x x 32 + 0 + 8 + 0 +2 + 1 = 43

Binary ‒to‒ Decimal Process The Process : Weighted Multiplication a) Multiply each bit of the Binary Number by it corresponding bitweighting factor (i. e. Bit-0→ 20=1; Bit-1→ 21=2; Bit-2→ 22=4; etc). b) Sum up all the products in step (a) to get the Decimal Number. Example: Convert the decimal number 01102 into its decimal equivalent. 0 1 1 0 23 22 21 20 8 4 2 1 0 + 4 + 2 + 0 Bit-Weighting Factors = 0110 2 = 6 10 610 4

Binary → Dec : Example #1 Example: Convert the binary number 100102 into its decimal equivalent. 5

Binary → Dec : Example #1 Example: Convert the binary number 100102 into its decimal equivalent. Solution: 1 0 0 1 0 24 23 22 21 20 16 8 4 2 1 16 + 0 + 2 + 0 = 1810 100102 = 1810 6

Binary → Dec : Example #2 Example: Convert the binary number 01101012 into its decimal equivalent. 7

Binary → Dec : Example #2 Example: Convert the binary number 01101012 into its decimal equivalent. Solution: 0 1 1 0 1 26 25 24 23 22 21 20 64 32 16 8 4 2 1 0 + 32 + 16 + 0 + 4 + 0 + 1 = 5310 01101012 = 5310 8

Binary → Dec : More Examples a) 0110 2 = ? b) 11010 2 = ? c) 0110101 2 = ? d) 11010011 2 = ? 9

Binary → Dec : More Examples a) 0110 2 = ? b) 11010 2 = ? 6 10 26 10 c) 0110101 2 = ? 53 10 d) 11010011 2 = ? 211 10 10

Hex values 0 1 2 3 4 5 6 7 8 9 A – 10 B - 11 C - 12 D - 13 E - 14 F - 15

Hex → Dec : Example #1 Example: Convert the binary number 5 D 16 into its decimal equivalent. Solution: A – 10 B - 11 C - 12 D - 13 E - 14 F - 15 12