# 1. Powers of Two

## 1.1. Find the result of the following and provide the answer in power of two

215 x 2-3 x 2-5

all in the power 15-8=7

=2^7

## 1.2. Find the result of the following and provide the answer in power of two

( 218 x 212 ) / ( 213 x 27 )

18+12=30 13+7=20 30-20=10 =2^10

# 2. Converting numbers between different bases

## 2.1. Convert (53)7 to octal (base 8) notation

5x7+3x1=38 base 10

4x8+6x1=38 base 10

46 base 8

## 2.2. Convert (BE)16 to binary

10*16+14*1=(174) base 10

(10101110) base2

# 3. The template method

## 3.1. Using the template method, convert 1011012 to its decimal equivalent

 1 0 1 1 0 1 25 24 23 22 21 20 ? ? ? ? ? ?

32+0+8+4+0+1=45

## 3.2. Using the template method, convert 14310 to its binary equivalent

(143)10 ⇒⇒ (10001111)2

## 3.3. Using the extended template method, convert 205.87510 to its binary equivalent

(205.875)10 ⇒⇒ (110011010.111)2

Almost. You have an extra 0 before the decimal point that should not be there. The correct ans is 1100 1101.111(-.5 pt)

# 4. Binary representation of numbers

## 4.1. What is the binary (base 2) number 100111111, written in decimal (base 10)?

(100111111)base2 ⇒⇒ (319) base10

## 4.2. What is the largest positive base 10 integer that can be represented with 15 bits?

1,000,000,000,000,000

Good try. However to find the largest positive number, use the formula 2N -1. Where N= the number of bits. So you will get 215 -1. Which is 32767 (base 10) (-1 pt)

128

## 4.4. How many bits are needed to represent the base-10 number 1021 ?

512+256+128+64+32+16+8+4+0+1

1111111101

10 bits

32

## 4.6. convert (168)10 to its binary equivalent

(10101000) base 2

# 5. INTEGER MULTIPLICATION AND DIVISION OF BINARY NUMBERS BY POWERS OF TWO

101011000

## 5.2. Divide 11100102 by 3210 and represent the result in binary

11

with Reminder=10010

(101001.101001)2

(10.0011)2

# 7. Binary Multiplication

(1100111001)2

## 7.2. Calculate (1010101)2 multiplied by (1024)10 (without using a calculator), and represent the result in integer binary.

10101010000000000

# 8. Use your creativity to generate 4 problems of your own and provide answers to them, to demonstrate your understanding of binary number conversion and binary number arithmetic.

## 8.1. Q1

Convert (AB) base 16 into a base 10

(AB)base16 ⇒⇒ (171)base10

## 8.2. Q2

Convert (112) base 10 into a binary number.

1110000

## 8.3. Q3

Multiply 1011011 x 100 = 101101100

## 8.4. Q4

Add 1011 + 1101 = 11000