Floating point binary number to a 7 segment decimal display

I have covered floating point (32 bit) conversion from float to decimal and decimal to float. I am happy with the theory and I have created a conversion tool in Excel VBA which works just fine following the IEEE754 , so I am happy with theory. Also happy with add, sub , mult , div of 32 bit floating point binary numbers. What I cannot understand or find anywhere online is the answer to this simple question. How do computers / calculators do the final conversion from the floating point binary number onto a display. For eaxmple , I have built a BCD to decimal converter using Logisim (combinational logic gates) and I have built a Binary to Decimal converter in Logisim using the Double Dabble algorithm si I can see how these can display on a set of 7 segment displays but how does the number (0 10000001 01 00 11 00 11 00 11 00 11 00 11 0) which is the floating point binary for decimal number 5.2 actually get converted using logic circuits.

How fast would a Tenser’s Floating Disk descend if I pulled it over a long drop?

So I’m designing a variant human warlock with the wizard ritual caster feat and while considering which rituals to start with I read the description for Tenser’s floating disk and looking through the eldritch invocations I saw the Ascendant step invocation allows levitation on myself at will so if I was to make a floating disk, have a party member or some equipment placed on it and then go down a chasm or hole or off the side of a flying ship/island etc would the disk follow at my levitate speed (20 feet descent or ascent per turn) or my movement speed (30 feet per turn) or would it drop like a rock? I’m picturing using it like a down elevator. Additionally would I be able to hold a wooden tabletop under the disk and levitate up and have it ascend to stay 3 feet above the surface?

For ease of reference here is the description of the relevant spells (quoted from D&D Beyond).

Tenser’s floating disk:

This spell creates a circular, horizontal plane of force, 3 feet in diameter and 1 inch thick, that floats 3 feet above the ground in an unoccupied space of your choice that you can see within range. The disk remains for the duration, and can hold up to 500 pounds. If more weight is placed on it, the spell ends, and everything on the disk falls to the ground.
The disk is immobile while you are within 20 feet of it. If you move more than 20 feet away from it, the disk follows you so that it remains within 20 feet of you. It can move across uneven terrain, up or down stairs, slopes and the like, but it can’t cross an elevation change of 10 feet or more. For example, the disk can’t move across a 10-foot-deep pit, nor could it leave such a pit if it was created at the bottom.
If you move more than 100 feet from the disk (typically because it can’t move around an obstacle to follow you), the spell ends.

Levitate:

One creature or loose object of your choice that you can see within range rises vertically, up to 20 feet, and remains suspended there for the duration. The spell can levitate a target that weighs up to 500 pounds. An unwilling creature that succeeds on a Constitution saving throw is unaffected.
The target can move only by pushing or pulling against a fixed object or surface within reach (such as a wall or a ceiling), which allows it to move as if it were climbing. You can change the target’s altitude by up to 20 feet in either direction on your turn. If you are the target, you can move up or down as part of your move. Otherwise, you can use your action to move the target, which must remain within the spell’s range.
When the spell ends, the target floats gently to the ground if it is still aloft.

To be clear I am not asking about whether I can move the disk over a hole, I am aware of that limitation and can easily put a plank over the hole and move the disk over the void, I am only asking about the vertical movement speed of the disk.

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How to create a floating social share without JS script in WordPress

I have created a social sharing button for my WordPress site with the help of some online tutorial and it works great. The sharing button perfectly appeared at the bottom of every post. Now I wanted a vertical and fixed floating social share bar for every post. How do I edit this code? so that the sharing button appears vertically on the side of each post. FYI WordPress is Genesis.

function gossip_social_sharing_buttons($  content) { global $  post; if(is_single() || is_home()){      // Get current page URL      $  gossipURL = urlencode(get_permalink());      // Get current page title     $  gossipTitle = htmlspecialchars(urlencode(html_entity_decode(get_the_title(), ENT_COMPAT, 'UTF-8')), ENT_COMPAT, 'UTF-8');     // $  gossipTitle = str_replace( ' ', '%20', get_the_title());      // Get Post Thumbnail for pinterest     $  gossipThumbnail = wp_get_attachment_image_src( get_post_thumbnail_id( $  post->ID ), 'full' );      // Construct sharing URL without using any script     $  twitterURL = 'https://twitter.com/intent/tweet?text='.$  gossipTitle.'&amp;url='.$  gossipURL.'&amp;via=ShoppersGossip';     $  facebookURL = 'https://www.facebook.com/sharer/sharer.php?u='.$  gossipURL;     $  pinterestURL = 'https://pinterest.com/pin/create/button/?url='.$  gossipURL.'&amp;media='.$  gossipThumbnail[0].'&amp;description='.$  gossipTitle;       // Add sharing button at the end of page/post content     $  content .= '<div class="gossip-social">';     $  content .= '<a class="gossip-link gossip-twitter" href="'. $  twitterURL .'" target="_blank" rel="noopener noreferrer nofollow">Twitter</a>';     $  content .= '<a class="gossip-link gossip-facebook" href="'.$  facebookURL.'" target="_blank" rel="noopener noreferrer nofollow">Facebook</a>';     $  content .= '<a class="gossip-link gossip-pinterest" href="'.$  pinterestURL.'" data-pin-custom="true" target="_blank" rel="noopener noreferrer nofollow">Pinterest</a>';     $  content .= '</div>';       return $  content; }else{     // if not a post/page then don't include sharing button     return $  content; }}; add_filter( 'the_content', 'gossip_social_sharing_buttons'); 

CSS

.gossip-link { padding: 6px 14px!important; color: #fff!important; font-size: 14px; border-radius: 3px!important; border-bottom: none!important; margin-right: 6px; cursor: pointer; margin-top: 2px; display: inline-block; text-decoration: none; font-weight: 700; }  .gossip-social { margin: 20px 0 40px; font-size: 14px; }  .gossip-link:hover { color: #fff; }  .gossip-twitter { background: #00aced; }  .gossip-twitter:hover { background: #0397d4; }  .gossip-facebook { background: #3B5997; }  .gossip-facebook:hover { background: #2d4372; }  .gossip-pinterest { background: #bd081c; }  .gossip-pinterest:hover { background: #9e0616; } 

Can anybody help, please?

Write the smallest positive number that can be represented by the floating point system

Using a normalised floating point representation box with an 8-bit mantissa and a 4-bit exponent, both stored using two’s complement.

(a) Write the smallest positive number that can be represented by the floating point system in the boxes below. The result is: Mantissa 0.1000000 and exponent 1000

Do not see how this can could someone please explain.

Do we need to check for mantissa overflow in floating point multiplication?

We do check for the mantisas overflow in floating point addition

e.g.

If we are adding $ 8.02 \times 10^3 + 9.01 \times 10^3 =17.03 \times 10^3$ i.e we get an overflow, so we shift the number right and increase the value of exponent.

But does it occurs during floating point multiplication?

According to my logic, it should occur. because $ 9.99\times9.99=99.80$ which is a mantissa overflow, but that’s not the case.

I have referred to Morris Mano’s books and William Wtallings Computer Organization and Architecture book but none of those books mentioned about floating-point multiplication mantissa overflow.

So I feel like I am wrong.

Please tell me where I am wrong?

Normalization in IBM hexadecimal floating point

According to the Wikipedia link of IBM hexadecimal floating point:

Consider encoding the value −118.625 as an IBM single-precision floating-point value.

The value is negative, so the sign bit is 1.

The value 118.62510 in binary is 1110110.1012. This value is normalized by moving the radix point left four bits (one hexadecimal digit) at a time until the leftmost digit is zero, yielding 0.011101101012. The remaining rightmost digits are padded with zeros, yielding a 24-bit fraction of .0111 0110 1010 0000 0000 00002.

The normalized value moved the radix point two digits to the left, yielding a multiplier and exponent of 16+2. A bias of +64 is added to the exponent (+2), yielding +66, which is 100 00102.

Combining the sign, exponent plus bias, and normalized fraction produces this encoding:

S Exp Fraction
1 100 0010 0111 0110 1010 0000 0000 0000
In other words, the number represented is −0.76A00016 × 1666 − 64 = −0.4633789… × 16+2 = −118.625

Now, the definition of normalization according to Wikipedia says that

In base $ b$ a normalized number will have the form $ ±d_0.d_1d_2d_3…×b_n$ where $ d_0≠0$ , and the digits $ d_0,d_1,d_2,d_3,…$ are integers between $ 0$ and $ b−1$

So, how is $ 0.011101101012 \times 16^2$ a normalized number?
In fact this number cannot be represented as a normalized one with base $ 16$ exponent because the closest we can get is $ 1.1101101012 \times 16^1 \times 2^2$ . What am I missing here?

What are the smallest and biggest negative floating point numbers in IEEE 754 32 bit?

I am stuck with a question that asks for smallest and biggest negative floating point numbers in IEEE 754 32-bit (their representation and decimal numerical value from which one can approximate the precision of the number)? So -0, NaN and Infinity do not belong to negative rational numbers.

I have stumbled upon -3.403 x 10^38 and 2^-126. I came close to the first one actually. I tried to do some calculations but got kind of lost in the process as floating point representation is counter-intutive for me, especially when calculating negative numbers. Can someone help me to clarify my thought process for the calculations so that I can find the numbers?