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100 binary

Binary Data

About[]

The binary numeral system, or base-2 number system represents numeric values using two symbols, usually 0 and 1. More specifically, the usual base-2 system is a positional notation with a radix of 2. Owing to its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used internally by all modern computers.

Simple Conversions

  • 1- 1
  • 10- 2
  • 11- 3
  • 100- 4
  • 101- 5
  • 110- 6
  • 111- 7
  • 1000- 8
  • 1001- 9
  • 1010- 10

Hex-Dec Conversion[]

Convert a hexadecimal number into its decimal; multiply the decimal equivalent of each hexadecimal digit by the corresponding power of 16 and add the resulting values:

Example1: C0E716

1. C = (12 × 163) = (12 × 4096) =49,152

2. 0 = (0 × 162) = (0 × 256) = 0

3. E = (14 × 161) = (14 × 16) = 224

4. 7 = (7 × 160) = (7 × 1) = 7

C0E716 = (12 × 163) + (0 × 162) + (14 × 161) + (7 × 160) = (12 × 4096) + (0 × 256) + (14 × 16) + (7 × 1) = 49,38310

or

C0E716 = 49,152 + 0 + 224 + 7 = 49,38310

Bin-Hex Conversion[]

Convert a binary number into its hexadecimal; divide into groups of four bits. If the number of bits isn't a multiple of four, simply insert extra 0 bits at the left (called padding).

Example1: 10100102 = 0101 0010 (grouped with padding) = 5216

Group1:

8 4 2 1
0 0 1 0

Answer: 0010 = 2

Group2:

8 4 2 1
0 1 0 1

Answer: 0101 = 5

0101 0010 = 5216

Example2: 110111012 = 1101 1101 grouped = DD16

Hex-Bin Conversion[]

Convert a hexadecimal number into its binary; substitute the corresponding binary digits:

Example1: 0011 1010 = 3A16

Group1:

8 4 2 1
0 0 1 1

Answer: 0011 = 3

Group2:

8 4 2 1
1 0 1 0

Answer: 1010 = A (10)


Example2: 1110 01112

Answer: E(14)716

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