Understanding Powers of Two and Binary

The video tutorial explains how to convert a decimal number, specifically 114, into its binary representation. It begins by introducing the concept of decomposing numbers into sums of powers of two. The tutorial then provides a step-by-step breakdown of the conversion process, demonstrating how to express 114 as a sum of powers of two: 64, 32, 16, and 2. Finally, it explains how to translate this decomposition into binary form, resulting in the binary number 1110010.

What is the first step in converting a decimal number to binary?

• Add the number to itself

• Divide the number by ten

• Decompose the number into the sum of powers of two

• Multiply the number by two

Which of the following is a power of two?

• 15

• 20

• 10

• 16

What is the largest power of two less than or equal to 114?

• 32

• 256

• 64

• 128

How can the number 50 be expressed as a sum of powers of two?

• 8 + 42

• 16 + 34

• 32 + 18

• 64 + 14

What is the binary place value for the number 16?

• Eight's place

• Two's place

• Sixteen's place

• Four's place

In binary, how many digits are used to represent numbers?

• One

• Two

• Three

• Four

How many 'ones' are there in the binary representation of 114?

• Zero

• One

• Two

• Three

What is the binary representation of the decimal number 114?

• 1110100

• 1011100

• 1110010

• 1101100

Which place value in binary represents the number of 64s in a number?

• Thirty-two's place

• Two's place

• Sixty-four's place

• One's place

What is the sum of powers of two that equals 114?

• 64 + 32 + 16 + 2

• 64 + 32 + 8 + 4

• 64 + 16 + 8 + 4 + 2

• 32 + 16 + 8 + 4 + 2