Exercise 2.1

Calculation

Number	Calculation
1.0	$(-1)^0 \times 2^{127-127} \times 1.0000 \dots 0$
2.0	$(-1)^0 \times 2^{128-127} \times 1.0000 \dots 0$
3.0	$(-1)^0 \times 2^{128-127} \times 1.1000 \dots 0$
4.0	$(-1)^0 \times 2^{129-127} \times 1.0000 \dots 0$
5.0	$(-1)^0 \times 2^{129-127} \times 1.0100 \dots 0$
6.0	$(-1)^0 \times 2^{129-127} \times 1.1000 \dots 0$
7.0	$(-1)^0 \times 2^{129-127} \times 1.1100 \dots 0$
8.0	$(-1)^0 \times 2^{130-127} \times 1.0000 \dots 0$
9.0	$(-1)^0 \times 2^{130-127} \times 1.0010 \dots 0$
10.0	$(-1)^0 \times 2^{130-127} \times 1.0100 \dots 0$

Verification

exercise_2_1.frag

#version 300 es precision highp float; precision highp int; out vec4 fragColor; uniform float u_time; uniform vec2 u_resolution; void main(){ vec2 pos = gl_FragCoord.xy / u_resolution.xy; pos *= vec2(32.0, 10.0); uint[10] a = uint[]( floatBitsToUint(1.0), floatBitsToUint(2.0), floatBitsToUint(3.0), floatBitsToUint(4.0), floatBitsToUint(5.0), floatBitsToUint(6.0), floatBitsToUint(7.0), floatBitsToUint(8.0), floatBitsToUint(9.0), floatBitsToUint(10.0) ); if (fract(pos.x) < 0.1){ if (floor(pos.x) == 1.0){ fragColor = vec4(1, 0, 0, 1); } else if (floor(pos.x) == 9.0){ fragColor = vec4(0, 1, 0, 1); } else { fragColor = vec4(0.5); } } else if (fract(pos.y) < 0.1){ fragColor = vec4(0.5); } else { uint b = a[int(pos.y)]; b = (b << uint(pos.x)) >> 31; fragColor = vec4(vec3(b), 1.0); } }

#version 300 es
precision highp float;
precision highp int;
out vec4 fragColor;
uniform float u_time;
uniform vec2 u_resolution;

void main(){
  vec2 pos = gl_FragCoord.xy / u_resolution.xy;
  pos *= vec2(32.0, 10.0);
  uint[10] a = uint[](
    floatBitsToUint(1.0),
    floatBitsToUint(2.0),
    floatBitsToUint(3.0),
    floatBitsToUint(4.0),
    floatBitsToUint(5.0),
    floatBitsToUint(6.0),
    floatBitsToUint(7.0),
    floatBitsToUint(8.0),
    floatBitsToUint(9.0),
    floatBitsToUint(10.0)
  );
  
  if (fract(pos.x) < 0.1){
    if (floor(pos.x) == 1.0){
      fragColor = vec4(1, 0, 0, 1);
    } else if (floor(pos.x) == 9.0){
      fragColor = vec4(0, 1, 0, 1);
    } else {
      fragColor = vec4(0.5);
    }
  } else if (fract(pos.y) < 0.1){
    fragColor = vec4(0.5);
  } else {
    uint b = a[int(pos.y)]; 
    b = (b << uint(pos.x)) >> 31;
    fragColor = vec4(vec3(b), 1.0); 
  }
  
}