Signed vs Unsigned Numbers

• Signed: the set of numbers includes negative numbers
• Unsigned: the set of numbers includes ONLY positive numbers

	Unsigned	Signed
0000	0	0
0001	1	1
0010	2	2
0011	3	3
0100	4	4
0101	5	5
0110	6	6
0111	7	7
1000	8	-8
1001	9	-7
1010	10	-6
1011	11	-5
1100	12	-4
1101	13	-3
1110	14	-2
1111	15	-1

NOTE

Signed numbers are using 2’s Complement system The most significant bit of the signed number still retains the value of that bit, but becomes a negative number instead 1000 → $-8$

IMPORTANT

There is no difference in the bit patterns between signed and unsigned number → programming languages need to interpret the number as either signed or unsigned types

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Practice Problem

#include <string.h>
#include <stdint.h>
#include <stdio.h>
 
// Take 32 ASCII characters that are 0 or 1
// Return a signed 32-bit integer
int32_t bin_to_dec_signed(char str[]){
	// Loop over the characters in the string from 0 to 31
	// Take the character at the next index
	// If '1', put a 1 in the least significant bit
	// If '0', leave that bit as 0
	// Then shift everything to the left by 1
	int32_t result = 0;
	for(int i = 0; i < 32; i++){
		result = result << 1;
		if(str[i] == '1'){ result = result | 1; }
		printf("Current result is: %b\n", result);
	}
	
	return result;
}
 
int main(){
	// read one line of typed input to get the ASCII string for this problem
	char input[33]; // enough space for 32 '0' or '1' characters followed by the '\0' bit
	fgets(input, 33, stdin);
	printf("Result: %d\n", bin_to_dec_signed(input));
	return 0;
}

• fgets: Wait until user types in input and press ENTER before continuing the rest of the program
  • input: The string variable to store the input
  • 33: How much characters to read in
  • stdin: The default input stream (terminal)