Binary Math

Question 1

Binary

Answer 1

A number system using only two digits, 1 and 0, representing on and off states in digital electronics.

Question 2

A Bit

Answer 2

The smallest unit of digital data, represented by a single binary value of either 1 or 0.

Question 3

A Byte

Answer 3

Often called an Octet, it consists of eight bits combined together to represent a single character of data.

Question 4

Binary to Decimal Conversion Chart

Answer 4

128 - 64 - 32 - 16 - 8 - 4 - 2 - 1

Each position doubles the previous value from right to left.

Question 5

What is Binary 00000010 in Decimal?

Answer 5

2 Decimal → Because the 1 falls on the second placeholder of the conversion chart, which equals 2.

Question 6

What is Binary 10000010 in Decimal?

Answer 6

130 Decimal → Because the 1 falls on the eighth and second placeholders of the conversion chart, which are 128 and 2, added together equals 130.

Question 7

What is Binary 11111111 in Decimal?

Answer 7

255 Decimal → Because the 1 falls on all eight placeholders of the conversion chart—128, 64, 32, 16, 8, 4, 2, and 1—added together equals 255.

Question 8

What is Binary 01010101 in Decimal?

Answer 8

85 Decimal → Because the 1 falls on the 64, 16, 4, and 1 placeholders of the conversion chart, which added together equals 85.

Question 9

What is Decimal 154 in Binary?

Answer 9

10011010 → You add up the placeholder numbers in an order that equals 154 by asking “Is 128 less than or equal to 154? Yes, bring down a 1. Is 128 + 64 (192) less than or equal to 154? No, bring down a 0,” and continue this until you get the full binary number.

Question 10

What is Decimal 75 in Binary?

Answer 10

01001011 → You add up the placeholder numbers that equal 75 by checking each value in order—64 + 8 + 2 + 1 = 75—placing a 1 for each included value and 0 for skipped values.

Question 11

What is Decimal 200 in Binary?

Answer 11

11001000 → You add up the placeholder numbers that equal 200 by including 128 + 64 + 8 = 200, marking 1s in those positions and 0s in others.

Question 12

What is Decimal 19 in Binary?

Answer 12

00010011 → You add up the placeholder numbers that equal 19 by including 16 + 2 + 1 = 19, marking 1s for those positions and 0s for others.

Question 13

Powers of Two

Answer 13

2⁰ = 1
2¹ = 2
2² = 4
2³ = 8
2⁴ = 16
2⁵ = 32
2⁶ = 64
2⁷ = 128
2⁸ = 256
2⁹ = 512
2¹⁰ = 1024