This article was originally published on bmf-tech.com.
Overview
A summary of calculation methods for converting between binary, decimal, and hexadecimal.
What is Weight
Before calculating, understand the concept of weight.
Weight refers to the number representing each digit.
ex. Decimal 1234
10^0*4 = 4
10^1*3 = 30
10^2*2 = 200
10^3*1 = 1000
sum 1234
10^0, 10^1, 10^2... are weights.
ex. Binary 1101
2^0*1 = 1
2^1*0 = 0
2^2*1 = 4
2^3*1 = 8
sum 13
2^0, 2^1, 2^2... are weights.
What is Radix
Binary is 2, decimal is 10, hexadecimal is 16.
Binary to Decimal
Multiply the weight by each digit and sum them all.
ex. 1010
2^0*0 = 0
2^1*1 = 2
2^2*0 = 0
2^3*1 = 8
sum 10
Decimal to Binary
Perform a slightly different division.
To convert from decimal to binary, divide by 2, if there is a remainder, it's 1, if not, it's 0, and finally arrange the remainders from the last calculation.
ex. 100
100/2 = 50 no remainder 0
50/2 = 25 remainder 0
25/2 = 12 no remainder 1
12/2 = 6 no remainder 0
6/2 = 3 remainder 1
3/2 = 1 remainder 1 // Stop when the last is 1
Arrange from the bottom 110100
Ans. 110100
Binary to Octal
Three binary digits equal 2^3=8
To convert binary to octal, divide into groups of three digits and calculate.
Finally, arrange the results of each calculation.
ex. 100100
100
2^0*0 = 0
2^1*0 = 0
2^2*1 = 4
sum 4
100
2^0*0 = 0
2^1*0 = 0
2^2*1 = 4
sum 4
Ans. 44
ex. 1100
100
2^0*0 = 0
2^1*0 = 0
2^2*1 = 4
sum 4
1
sum 1
Ans. 14
Octal to Binary
Represent each digit as a three-digit binary number. Finally, omit leading zeros.
ex. 117
7 → 111
1 → 001
1 → 001
001001111 → 100111
Ans. 100111
Binary to Hexadecimal
Four binary digits equal 2^4=16
To convert binary to decimal, divide into groups of four digits and calculate.
Finally, arrange the results of each calculation.
Hexadecimal
0 1 2 3 4 5 6 7 8 9 A B C D E F 10
Decimal
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
ex. 11001100
1100
2^0*0 = 0
2^1*0 = 0
2^2*1 = 4
2^3*1 = 8
sum 12 → C
1100
2^0*0 = 0
2^1*0 = 0
2^2*1 = 4
2^3*1 = 8
sum 12 → C
Ans. CC
ex. 1100
1100
2^0*0 = 0
2^1*0 = 0
2^2*1 = 4
2^3*1 = 8
sum 12 → C
Ans. C
Hexadecimal to Binary
Represent each digit as a four-digit binary number. Finally, omit leading zeros.
ex. 8B6
6 → 0110
B → 1011
8 → 1000
Ans. 100010110110
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