Number System Conversions

Why are binary and hex critical in avionics?

Used in data buses, maintenance computers, and fault codes.

The 3 major number conversions in avionics

Decimal ↔ Binary, Decimal ↔ Hexadecimal, and Binary ↔ Hexadecimal.

Symbols used in the Binary number system

Only 0 and 1.

List the 8-bit position values for powers of 2 (highest to lowest)

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

Binary equivalent of 2⁰

1

Binary equivalent of 2¹

2

Binary equivalent of 2²

4

Binary equivalent of 2³

8

Binary equivalent of 2⁴

16

Binary equivalent of 2⁵

32

Binary equivalent of 2⁶

64

Binary equivalent of 2⁷

128

Decimal to Binary: Convert 13 to binary

00001101

How many symbols are used in the Hexadecimal system?

Sixteen symbols (0-9 and A-F).

Hex conversion: What value does letter 'A' represent?

10

Hex conversion: What value does letter 'B' represent?

11

Hex conversion: What value does letter 'C' represent?

12

Hex conversion: What value does letter 'D' represent?

13

Hex conversion: What value does letter 'E' represent?

14

Hex conversion: What value does letter 'F' represent?

15

Decimal to Hex: Convert 47 to hex

2F (47 ÷ 16 = 2 remainder 15)

Decimal to Hex: Convert 255 to hex

FF (255 ÷ 16 = 15 remainder 15)

Golden Rule: How do you convert Binary directly to Hexadecimal?

Split the binary number into groups of 4 bits.

Convert 4-bit binary '1010' to hex

A (10)

Convert 4-bit binary '1111' to hex

F (15)

Binary to Hex: Convert 10101111 to hex

AF (1010 = A, 1111 = F)

Binary to Hex: Convert 00111100 to hex

3C (0011 = 3, 1100 = C)

Convert 4-bit binary '0000' to hex

0

Convert 4-bit binary '0001' to hex

1

Convert 4-bit binary '0010' to hex

2

Convert 4-bit binary '0011' to hex

3

Convert 4-bit binary '0100' to hex

4

Convert 4-bit binary '0101' to hex

5

Convert 4-bit binary '0110' to hex

6

Convert 4-bit binary '0111' to hex

7

Convert 4-bit binary '1000' to hex

8

Convert 4-bit binary '1001' to hex

9

Convert 4-bit binary '1011' to hex

B

Convert 4-bit binary '1100' to hex

C

Convert 4-bit binary '1101' to hex

D

Convert 4-bit binary '1110' to hex

E

Convert 8-bit binary '00000000' to hex

00

Convert 8-bit binary '00000001' to hex

01

Convert 8-bit binary '00001010' to hex

0A

Convert 8-bit binary '00001111' to hex

0F

Convert 8-bit binary '00010000' to hex

10

Convert 8-bit binary '00111111' to hex

3F

Convert 8-bit binary '01010101' to hex

55

Convert 8-bit binary '10101010' to hex

AA

Convert 8-bit binary '11111111' to hex

FF

Practice: Convert 25 (decimal) to binary

00011001

Practice: Convert 10110110 (binary) to hexadecimal

B6 (1011 = B, 0110 = 6)

Practice: Convert 62 (decimal) to hexadecimal

3E (62 ÷ 16 = 3 remainder 14)

Practice: Convert 7F (hex) to decimal

127 ((7 × 16) + 15)

Practice: Convert 11110000 (binary) to hexadecimal

F0 (1111 = F, 0000 = 0)