2.11 Conversion between binary and decimal numbers

A. Introduction

Turn a binary number into decimal is easy: just multiply each digit with its place value and add up. e.g. 1101 = 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 8+4+1=13

B. Two ways to turn decimal into binary:

1. Divide the number by 2 until the quotient is 0, then write down all the remainder backwards.

2. Descending power of 2 and subtract:

1. Find the largest power of 2 that can fit in the decimal number x, let that be n. If x>2^n, note down 1 (from highest to lowest, i.e. left to right) otherwise note down 0.

2. x = x - 2^n

3. n=n-1 if n>=0, go back to step 1; otherwise done.

C. Try:

• Convert the following binary numbers into decimal numbers:

1011, 1101, 1111, 10001, 11001, 1100010011, 1000111011.

• Convert the following decimal numbers into binary numbers:

123, 789, 9021, 8762, -1000000, 0.5