Does SHA256 favor integers?

Question

While coding earlier I noticed something strange about SHA256, in that it seems to generate more integers than letters for the hash. At first I thought I was just imagining it, so I put together a quick test to make sure. Astonishingly, my test seems to prove that SHA256 favors integer values in the hash that it generates. I want to know why this is. Shouldn't the difference between a hash index being a letter and a number be the exact same? Here is my testing example:

namespace TestingApp
{
    static class Program
    {
        private static string letters = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ1234567890";
        private static char[] characters = letters.ToCharArray();
        private static Random _rng = new Random();

        static void Main(string[] args)
        {
            int totalIntegers = 0;
            int totalLetters = 0;
            for (int testingIntervals = 0; testingIntervals < 3000; testingIntervals++)
            {
                string randomString = NextString(10);
                string checksum = DreamforceChecksum.GenerateSHA256(randomString);
                int integerCount = checksum.Count(Char.IsDigit);
                int letterCount = checksum.Count(Char.IsLetter);
                Console.WriteLine("String: " + randomString);
                Console.WriteLine("Checksum: " + checksum);
                Console.WriteLine("Integers: " + integerCount);
                Console.WriteLine("Letters: " + letterCount);
                totalIntegers += integerCount;
                totalLetters += letterCount;
            }
            Console.WriteLine("Total Integers: " + totalIntegers);
            Console.WriteLine("Total Letters: " + totalLetters);
            Console.Read();
        }

        private static string NextString(int length)
        {
            StringBuilder builder = new StringBuilder();
            for (int i = 0; i < length; i++)
            {
                builder.Append(characters[_rng.Next(characters.Length)]);
            }
            return builder.ToString();
        }
    }
}

and my checksum/hashing class:

using System;
using System.Collections.Generic;
using System.Linq;
using System.Security.Cryptography;
using System.Text;
using System.Threading.Tasks;

namespace DreamforceFramework.Framework.Cryptography
{
    public static class DreamforceChecksum
    {
        private static readonly SHA256Managed _shaManagedInstance = new SHA256Managed();
        private static readonly StringBuilder _checksumBuilder = new StringBuilder();
        public static string GenerateSHA256(string text)
        {
            byte[] bytes = Encoding.UTF8.GetBytes(text);
            byte[] hash = _shaManagedInstance.ComputeHash(bytes);
            _checksumBuilder.Clear();
            for (int index = 0; index < hash.Length; index++)
            {
                _checksumBuilder.Append(hash[index].ToString("x2"));
            }
            return _checksumBuilder.ToString();
        }

        public static byte[] GenerateSHA256Bytes(string text)
        {
            byte[] bytes = Encoding.UTF8.GetBytes(text);
            byte[] hash = _shaManagedInstance.ComputeHash(bytes);
            _checksumBuilder.Clear();
            for (int index = 0; index < hash.Length; index++)
            {
                _checksumBuilder.Append(hash[index].ToString("x2"));
            }
            return Encoding.UTF8.GetBytes(_checksumBuilder.ToString());
        }

        public static bool ValidateDataIntegrity(string data, string targetHashcode)
        {
            return GenerateSHA256(data).Equals(targetHashcode);
        }
    }
}

I have ran my test multiple times, and every time it seems that more integers are generated within the hash than letters. Here are 3 test runs:

Does anyone know why SHA256 seems to favor numbers instead of an equal distribution of both letters and numbers?

Answer 1

Given that there are 10 digits and 6 letters possible, the proportion should be roughly 10:6. That's right in line with your results.

Answer 2

The output is hexadecimal. 0-9 and a-f